CBSE Class 12

Detailed, Step-by-Step NCERT Solutions for 12 Accountancy Chapter 11 Cash Flow Statement Questions and Answers were solved by Expert Teachers as per NCERT (CBSE) Book guidelines covering each topic in chapter to ensure complete preparation.

Cash Flow Statement NCERT Solutions for Class 12 Accountancy Chapter 11

Cash Flow Statement Questions and Answers Class 12 Accountancy Chapter 11

Test your Understanding-1 (Page No. 287)

Classify the following activities into operating activities, investing activities, financing activities, cash activities.
1. Purchase of machinery
2. Proceeds from issuance of equity share capital
3. Cash Sales
4. Proceeds from long-term borrowings .
5. Proceeds from sales of old machinery
6. Cash receipt from debtors
7. Trading commission received
8. Purchase of investment
9. Redemption of preference shares
10. Cash purchase
11. Proceeds from sale of Investment
12. Purchase of goodwill
13. Cash paid to supplier
14. Interim dividend paid on equity shares
15. Wages and salaries paid .
16. Proceeds from sale of patents
17. Interest received on debentrues held as investments
18. Interest paid on long-term borrowings
19. Office and administrative expenses paid
20. Manufacturing overhead paid
21. Dividend received on shares held as investment
22. Rent received on property held as investment
23. Selling and distribution expenses paid
24. Income tax paid
25. Dividend paid on preferences shares
26. Underwriting commission paid
27. Rent paid –
28. Brokerage paid on purchase of investment
29. Bank overdraft
30. Cash credit ‘
31. Short-term deposit
32. Marketable securities
33. Refund of income-tax received.
Answer:
(a) Operating Activities—
3. Cash sales
6. Cash .receipts from debtors
7. Trading commission Received
10. Cash purchases
13. Cash paid to supplier
15. Wages and salaries paid
19. Office and administrative expenses
20. Manufacturing overhead paid
23. Selling and distribution expenses paid
24. Income tax paid
27. Rent paid

(b) Investing Activities—
1. Purchase of machinery
5. Proceeds from sale of old machinery
8. Purchases of investment
11. Proceeds from sale of investment
12. Purchase of goodwill
16. Proceeds from sale of patents
17. Interest received on debentures held as investments
21. Dividend received on shares held as investment
22. Rent received on property held as investment
29. Bank overdraft

(c) Financing Activities—
2. Proceeds from issunace of equity share
4. Proceeds from long-term borrowing
9. Redemption of preference shares
14. Interim dividend paid on equity shares
18. Interest paid on long-term borrowings
25. Dividend paid on preferences shares
26. Underwriting commission paid
28. Brokerage paid on purchase of investment

(d) Cash Equivalents—
30. Cash credit
31. Short-term deposit
32. Marketable securities
33. Refund of income-tax received.

Test your Understanding-11 (Page No. 297-298)

Question 1.
Choose one of the two alternatives given below and fill in the blanks in the following statements:
(a) If the net profits earned during the year is Rs. 50,000 and the amount of debtors in the beginning and the end of the year is Rs. 10,000 and Rs. 20,000 respectively, then the cash from operating activities will be equal to Rs (Rs. 40,000/Rs. 60,000)
(b) If the net profits made during the year are Rs. 50,000 and the bills receivables have decreased by Rs. 10,000 during the year then the cash flow from operating activities will be equal to Rs (Rs. 40,000/Rs.60,000)
(c) Expenses paid in advance at the end of the year are the profit made during the year (added to/deducted from).
(d) An increase in accrued income during the particular year is the net profit (added to/deducted from.)
(e) Goodwill written off is the profit made during the year for calculating the cash flow from operating activities (added to/deducted from)
(f) For calculating cash flow from operating activities, provision for doubtful debts is the profit made during
the year (added to/deducted from).
Answer:
(a) Rs. 40,000
(b) Rs. 60,000
(c) deducted from
(d) deducted from
(e) added to
(f) added to

Question 2.
While computing cash from operating activities, indicated whether the following items will be added or subtracted from the net profit—if not to be considered write NG.

Answer:
(a) Increase in the value of creditors will be added to net profit, while computing cash from operating activities.
(b) Increase in the Value of patents will not to be considered (NC) while computing cash from operating activities.
(c) Decrease in prepaid expenses will be added to the net profit while computing cash from operating activities.
(d) Decrease in income received in advance will be subtracted
from the net profit while computing cash from operating activities.
(e) Decrease in value of stock will be added to the net profit while computing cash from operating activities.
(f) Increase in Share Capital will not to be considered (NC) while computing cash from operating activities.
(g) Increase in the value of bills receivables will be subtracted from the net profit while computing cash from operating activities.
(h) Increase in the amount of outstanding expenses will be added to the net profit while computing cash from operating activities.

(i) Conversion of debenture into share will not be considerd (NC) while computing cash from operating activities.
(j) Decrease in the value of bills payables will be subtracted from the net. prof it while computing cash from operating activities.
(k) Increase in the value of debtors will be subtracted from net profit while computing the cash from operating activities.
(l) Decrease in the amount of accrued income will be added to net profit while computing the cash from operating activities.

Do it Yourself (Page No. 296-297)

Question 1.
The Profit and Loss Account of Raj Limited is given here under:


Ascertain Cash from Operations. Show your workings clearly.
Answer:
Cash Flows from Operating Activities

Working Note
1. Net Profit before taxation and extra-ordinary item
= Rs. 15,80,000 + Rs. 8,00,000

2.

Question 2.
From the following information calculate net cash from operations:

Answer:

Do it Yourself (Page No. 300-301)

Question 1.
From the following particulars, calculate cash flows from investing activities:

Interest received on debentures held as investment Rs. 60,000
Dividend received on shares held as investment Rs. 10,000
A plot of land had been purchased for investment purposes and was let out for commercial use and rent received Rs. 30,000.
Answer:
Cash Flow from Investing Activities

Question 2.
From the following information, calculate cash flows from investing and the financing activities

In year 2006, machine costing Rs. 2,00,000 was sold at a profit of Rs. 1,50,000, Depreciation charged on machine during the year 2006 amounted to Rs. 2,50,000.
Answer:

Short Answer Type Questions

Question 1.
What is a Cash Flow Statement?
Answer:
Cash Flow Statements—-Cash Flow Statement is a statement which shows Inflows (receipts) and Outflows (payments) of cash and its equivalents in an enterprise during a specified period of time. Accounting Standard (AS-3) Revised issued by the Institute of Chartered Accountant of India on Cash How Statement in March 1997 has defined Cash Flow Statement as “A statement which shows inflows (receipts) and outflows (payment) of cash and its equivalents in an enterprise during a specified period of time.”

According to the Revised Accounting Standard 3, an enterprise should prepare a cash flow statement and should present it for each period for which financial statements are presented.

The terms, Cash, Cash-Equivalents and Cash Flows explained below:

Cash: It comprises cash in hand and demand deposits with bank.

Cash-Equivalents: They are short term highly liquid investments that are readily convertible into cash and which are subject to an insignificant risk of change in value. An investment normally qualifies as cash equivalent only when it has a short maturity, of say three months or less from the date of acquisition. Cash equivalent are held for the purpose of meeting short term cash commitments rather than for investment or other purpose.

Cash-Flows : These are inflows and outflows of cash and cash- equivalents. An inflows increases the total cash and cash-equivalents at the disposal of the enterprise whereas an outflow decrease them.

As per AS-3, cash flows exclude movements between items that contribute cash or cash equivalents because these components are part of the cash management of an enterprise rather than part of its operating, investing or financing activities.

Benefits of Cash Flow Statement:
Cash Flow Statement is a useful financial statement and provides the following benefits:
(a) It enables the management to identify the magnitude and directions of changes in cash.

(b) It enables the users to evaluate the changes in economic resources of an enterprise.

(c) It enables the users to evaluate the changes in financial structure.

(d) It enables the users to evaluate the changes in net assets of an enterprises.

(e) It enables the users to evaluate the enterprise’s ability to alter the amounts and timings of cash flows in order to adapt to changing circumstances and opportunities.

(f) It is useful in assessing the ability of the enterprise to generate Cash and Cash Equivalents and enables users to develop models to assess and compare the present value of the future cash flows of different enterprises.

(g) As a tool of planning, the projected Cash Flow Statement enables the management to plan its future investment, operating and financial activities such as repayment of long term loans and interest there on, modernisation or expansion of plant, payment of cash dividend etc.

(h) It helps in efficient cash management. The management can know the adequacy or other wise of cash and can plan for the effective use of surplus cash or can make the necessary arrangement in case of an inadequacy of Cash.

(i) It also enhances the comparability of the reporting of operating performance by different enterprises because it eliminate the effects of using different accounting treatments for the same trasactions and events.

Question 2.
How the various activities are classfied (as per AS-3 revised) while preparing cash flow statement?
Answer:
Classification of Cash Flows :
A cash flow statement shows inflow and outflow of cash and cash equivalents from various activities of a company during a specific period. As per AS-3, these activities can be classified in to three categories which are following :
1. Operating Activities
2. Investing Activities
3. Financing Activities

1. Operating Activities—Operating activities are the principal
revenue producing activities of the enterprise and other activities that are not investing or financing activities. Cash flows from operating activities generally result from the transactions and other events that enter into the determination of net profit or loss. The amount of cash flows arising from operating activities is a key indicator of the extent to which the operations of the enterprise have generated sufficient cash flows to maintain the operating capability of the enterprise to pay dividend, repay loans and make investments without resources to extent source of financing.

2. Investing Activities—As per AS-3 Investing activities are the acquisition and disposal of long-term assets (such as land, building, plant, machinery etc.) and other investment not included in cash equivalent. It is important to make a separate disclosure of cash flows arising from investing activities because the cash flows represent the extent to which expenditures have been made for resources intended to generate future income and cash flows.

3. Financing Activities—As per AS-3, Financing activities are activities that result in changes in the size and composition of the owner’s capital (including preference share capital in the case of a company) and borrowings of the enterprise. The separate disclosure of cash flows from financing activities is important because it is useful in predicting claims on future cash flows by providers of funds (both capital and borrowings) to the enterprise.

Question 3.
State the uses of cash flow statement?
Answer:
Along with balance sheet and income statement, the statement of cash flows would assists the users of financial statements in the following way :
1. To analyse the reasons for change in cash balance of the enterprise.
2. To judge the enterprise ability to pay its debts, to pay dividends to its shareholders and to pay interest on loans.
3. To assess the enterprise’s need to borrow cash.
4. To find out the reasons for difference between the enterprise net income, cash payment and cash receipts.
5. To analyse reasons for change in enterprise’s financial position including investing and financial activities during a period of time.

Question 4.
What are the objectives of preparing cash flow statement?
Answer:
Objectives of Cash Flow Statement:
The basic objectives of Cash Flow Statement is to highlight the change in the cash position including the sources from which cash was obtained by the enterprise and specific uses to which cash was applied. The cash flow statement serves a number of objectives which are following:

1. Depict Inflows and Outflows of Cash :
Cash flow statement gives information about cash inflows and cash outflows of an enterprise during a particular period from operating activities, investing activities and financing activities. It is an effective tool of managing cash.

2. Cash flow information helps in Planning :
Cash flow statement provide information for planning for short range cash needs of the enterprise. It helps in formulation of financial policies.

3. Helping in understanding the Liquidity of the Enterprise : Cash Flow Statement helps the enterprise to assess whether it would meet its current obligation or not. It also helps the lending institution like banks etc. to ascertain the liquidity of the enterprise.

4. Help pi preparing Cash Budget:
Cash Flow Statement helps the management of the firm in preparing Cash Budget.

5. Analysis Management of cash :
Cash flow statement reveal good and bad points relating to the management of cash.
According to AS-3 (Revised) the objectives of cash flow statement are as follows : “Information about the cash flow of an enterprise is useful in providing users of financial statement with a basis to assess the ability of the enterprise to generate cash and cash equivalent and the needs of the enterprise to utilise these cash flows.

The economic decisions that are taken by users require an evaluation of the ability of an enterprise to generate cash and cash equivalents and the timing and certainty of their generation. The statement deals with the provision of information about the historical changes in cash and cash equivalent of an enterprise by means of a cash flow statement which classifies cash flows during the period from operating, investing and financing activities.

Question 5.
Explain the terms: Cash Equivalents, Cash Flows.
Answer:
(i) Cash Equivalents—They are short term highly liquid investments that are readily convertible into cash and which are subject to an insignificant risk of change in value. An investment normally qualifies as cash equivalents only when it has a short term maturity, of say three months or less from the date of acquisition.

Cash equivalent are held for die purpose of meeting short term cash commitments rather than for investment or other purpose. Examples of cash equivalents are treasury bills, commercial papers etc. which are purchased with cash that is in excess of immediate needs.

(ii) Cash Flows—Cash Hows are inflows and outflows of cash and cash equivalents. An inflow increases the total cash and cash equivalents at the disposal of the enterprise where as an outflow decreases them. As per AS-3, Cash Flow include movements between items that constitute cash or cash equivalents because the components are part of the cash management of an enterprise rather than part of operating, investing or financing activities.

Question 6.
Prepare a format of cash flow from operating activities under direct method and indirect-method.
Answer:
Cash Flows From Operating Activities—Operating activities are the main source of revenue and expenditure in an enterprise. Therefore,the ascertainment of Cash Flows From Operating Activities is of prime importance.

As per AS-3, an enterprise should report Cash Flow From Operating Activities using either by
Direct Method
OR
Indirect Method
In direct method, major classes of gross cash receipts and gross cash payments are disclosed.
OR
In indirect method, net profit or loss is adjusted for the effects of
(i) transaction of a non-cash nature.
(ii) any deferrals or accruals of past/future operating Cash receipts.
(iii) Items of income or expenses associated with investing or financing cash flows.

Direct Method
As we know that items are recorded on accrual basis in Profit and Loss Account therefore certain adjustments are made to convert them into cash basis. These adjustments are discussed below :
1. Cash Inflow from Sales—Total Sales include Cash Sale and Credit Sale both. Cash sales is a cash inflow, but in case of credit sales, cash receipts from Debtors is calculated as follows—
Cash receipts from Customers
= Credit Sales + Opening Debtors and Bills Receivable – Closing Debtors and Bills Receivable – Bad Debts – Discount Allowed – Sales Returns.

2. Cash Ouflow from Purchases—Total Purchases include both cash purchases and credit purchases. Cash purchases are cash outflow, but in case of credit purchases, cash paid to the suppliers is calculated as follows—
Cash paid to Suppliers = Credit purchases + Opening
Creditors and Bills Payable – Closing Creditors and Bills Payable – Discount received – Purchases Returns.
Purchases = Cost of Goods sold – Opening Stock + Closing Stock

3. Cash Outflow on Expenses Incurred—The figures of expenses given in the Profit and Loss Account have to be adjusted to find out cash outflow. The amount outstanding and the amount paid in-advance have to be adjusted for this purpose.

Cash paid for Expenses = Expenses as given in Profit & Loss A/c – Prepaid Expenses in begining and Outstanding Exp. at the end + Prepaid Expenses at the end and Outstanding Expenses in the begining.

However, following items are not to be considered—
1. All non-cash items are ignored as no cash is involved in them. Examples are—
(a) Depreciation
(b) Discount on Issue of Shares written off
(c) Goodwill written off
(d) Preliminary Expenses written off
(e) Discount on Issue of Debenture written off
(f) Patents and Copyright written off
(g) Underwriting commission written off.

2. Appropriations of tiansfer to different reserves and provision like to General Reserve, Provision for Taxation and Proposed Dividend should be ignored.

3. Items which are classified as investing or financing activities like profit or loss on sale of fixed assets, interest received, dividend paid etc are also ignored.

Indirect Method
In this method, net profit or loss is adjusted for the effects of transactions of a non-cash nature flow. In other words, Net profit or loss is adjusted for items which affected net profit but did not affect cash.

As per AS-3, (Revised), under indirect method, net cash flow from operating activities is determined by adjusting net profit or loss for the effects of:

1. Non-cash items are to be added back. Non-cash items like
(a) Depreciation
(b) Goodwill written off
(c) Patents and Copyrights written off
(d) Appropriation to General Reserve
(e) Interim dividend
(f) Deferred taxes etc.

2. All other items for which the cash effects are investing or financing cash flows. The treatment of such items depend upon their nature. All investing and financing incomes are to be deducted, from the amount of net profits while all such expenses are to be added back.

3. Changes in current assets and liabilities during the period. Increase in current assets and decrease in current liabilities are to be deducted while increase in current liabilities and decrease in current assets are to be added up.

Question 7.
Now that you know the meaning of operating activities, state clearly what would constitute the operating activities for the following types of enterprises :
(1) Hotel
(ii) Film production house
(iii) Financial enterprise
(iv) Media enterprise
(v) Steel manufacture unit
(iv) Software business unit
Answer:
(i) Hotel (1) Payment of salary and wages to staff.
(2) Payment for the electricity, water, vegetables and other items for the Hotel.
(3) Payment for the items purchase for the Hotel accomodation.
(4) Receipts from the customer for staying in Hotel.
(5) Receipts from the other companies for taking Hotel for rent.

(ii) Film production house—Payment for the set, staff, actors and actress, director, music directors etc. Receipt from the distibutors for selling rights of the film.

(iii) Financial Enterprises—Payment for the loan, buying shares and payment for dividend and interest.
Receipt for the repayment of loan, interest, dividend etc.

(iv) Media Enterprise—Payment to the staff, reporters, photographers etc.
Receipts from the companies who advertise their products through media.

(v) Steel manufacturing unit—Payment for the raw material (iron), salary and Wages for staff, coal and other materials. Receipts from the market by selling steel.

(vi) Software business unit—Payment of salary to their staff. Receipts from the customer for selling their softwares and maintaining their computers.

Question 8.
“The nature/type of enterprise can change altogether the category into which a particular activity may be classified.” Do you agree? Illustrate your answer.
Answer:
Yes, it is true that the nature/type of enterprise can change altogether the category into which a particular activity may be classified. For example, in case of a financial enterprise (whose main business is lending and borrowing), interest paid, interest-received and dividend received are classified as operating activities while dividend paid is the financing activity but in case of a non-financial enterprise, as per AS-3, it is considered more appropriate that payment of interest and dividend paid are classified as financing activities whereas receipt of interest and dividends are classified as investing activities.

Long Answer Type Questions

Question 1.
Describe the procedure to prepare Cash Flow Statement.
Answer:
Procedure of preparation of Cash Flow Statement—The Institute of Chartered Accountants of India has issued Accounting Standard (AS-3) Revised, for preparing a Cash Flow Statement. This Accounting Standard has been made mandatory in repect of accounting periods commencing on or after 1st April, 2001, for certain enterprises. These enterprises are:

(i) Enterprises whose equity or debt securities are listed on a recognised stock exchange in India, and enterprises that are in process of isuing equity or debt securities that will be listed on a recognised Stock Exchange in India.

(ii) All other commercial, industrial and business enterprises, whose turnover for the accounting period exceeds Rs. 50 Crores. As such, the cash flow statement has been prepared according to AS-3 Revised. According to AS-3 Revised, the cash flow statement summarizes the cash inflows and cash outflows and the net changes (increase or decrease) in cash and cash equivalents resulting from operating, investing and financial activities of a firm duririg a period.

The following terms are used for preparing a cash flow statement:
Cash: It comprises cash in hand and demand deposits with banks.

Cash Equivalents—These are short-term, highly liquid investments that are readily convertible into known amounts of cash and which present insignificant risk of changes in their values. Normally, an investment will be termed as cash equivalent only if it has a short maturity period, say three month or less, from the date of its acquisition.

Examples of cash equivalents are treasury bills, commercial papers etc. which are purchased with cash that is in excess of immediate needs. Investment in shares are excluded from cash equivalents unless they are cash equivalents in reality.

For example the preference shares of a company which are purchased shortly before their redemption date will be included in cash equivalents provided there is only an insignificant risk of failure of the company in repaying the amount at the date of maturity.

Classification of Cash Flow—According to AS-3 (Revised), a cash flow statement should be presented in a manner that it reports inflows and outflows of cash by classifying them into three categories, namely : operating, investing and financing activities.

Classification of all activities into these three categories helps the users of cash flow statement to assess the effect of these activities on the cash and cash equivalents of the enterprise. Such information will be helpful in evaluating the relationship among these three activities. These three activities are explained as below :

(i) Cash Flow from Operating Activities—Operating activities are the main revenue generating activities of an enterprises. As such they include cash flows from those transactions and events which enter into the ascertainment of net profit or loss of the enterprise. Examples of cash flows arising from operating activities are :
(a) Cash receipts from the sale of goods and rendering of services
(b) Cash receipts from royalities, fees, commissions and other revenue
(c) Cash payment to suppliers for goods and services
(d) Cash payment to and on behalf of employees
(e) Cash receipts and cash payments of an insurance enterprise for premiums and claims, annuities and other policy benefits
(f) Cash payments or refunds of income taxes unless they can be specifically identified with financing and investing activities; and
(g) Cash receipts and payments relating to future contracts, forward contracts, option contracts and swap contracts when the contracts are held for dealing or trading purposes.

(ii) Cash Flow from Investing Activities—Investing activities include the purchase and sale of long-term assets such as land, buildings, plant and machinery etc. not held for resale. These activities also include the purchase and sale of such investments which are not inlcuded in cash equivalents. Cash flow from investing activities discloses the expenditures incurred for resources intended to generate future income and cash flows. Examples of such cash flows arising from investing activities are:

(a) Cash payment to aquire fixed assets (including intangibles) and also payments for capitalised research and development costs and self constructed fixed assets
(b) Cash receipts from sale of fixed assets (including intangibles)
(c) Cash payments to aquire shares, warrants or debt instruments of other enterprises (other than payments for those instruments considered to be cash equivalents);
(d) Cash receipts from sale of shares, warrants or debt instruments of other enterprises (other than receipts for those instruments considered to be cash equivalent);
(e) Cash advances and loans made to third parties (other than advances and loans made by a financial enterprise).
(f) Cash receipts from the repayment of advances and loan made to third parties (other than advances and loans of a financial enterprise);
(g) Cash payments for future contracts, forward contracts, option contracts and swap contracts except when the contracts are held for dealing or trading purposes, or the payments are classified as financial activities;
(h) Cash receipts of insurance claim for property involved in accident; and
(i) Cash receipts of interest and dividend.

(iii) Cash Flows from Financing Activities—Financing activities are the activities that result in change in capital’and borrowings of the enterprise. Examples of cash flows arising from financial activities are—
(a) Cash receipts from issuing shares or other similar instruments;
(b) Cash receipts from issuing debentures, loans, notes, bonds and other short term or long term borrowings;
(c) Cash repayments of amounts borrowed, buy-back of equity shares, redemption of preferene shares, debentures, notes, bonds etc., and
(d) Cash payment of interest and dividend.

Question 2.
Describe ‘Direct’ and ‘Indirect’ method of ascertaining cash flows from operating activities.
Answer:
Cash from Operating Activities—The net income is computed on the basis of accrual. To compute cash provided by operating activities we need to convert the operating activities being considered from accrual basis to cash basis. For this purpose, we can follow either ‘Direct Method’ or ‘Indirect Method’. The cash provided will be same, whatever method is used for computation. Accounting Standard 3 allows both methods for reporting cash from operating activities among Indian Companies.

Cash from Operating Activities-Direct Method—Under this method, we need to adjust each item in the income statement from accrued basis to cash basis. Cash receipts and cash payments related to revenues and expenses are determined and listed as cash inflows and outflows from operating activities. The net amount is reported in the last column as cash provided from operations.

Step 1: Determine cash provided by operating activities
(i) Cash receipts from customers : The revenue from sales is reported on accrual basis in the income statement. We add the amount of opening receivables to the net sales and to this we subtract amount or receivable at the end, bad debts written-off during the period and discount allowed to customers.

(ii) Other cash receipts—The amount of other revenue like rent, income, commission earned, etc. are adjusted for any amounts not received or received in advance to determine cash received.

Step 2: Cash used in operating activities :
(i) Cash payment to suppliers—The income statement reports cost of goods sold on accrual basis. To determine the cash paid to suppliers, we need to first ascertain purchases. The closing stock of goods is added to cost of goods sold and opening stock is subtracted there from to compute the purchases during the period.

We need to add the creditors (Account Payables) in the beginning of the period to the amount of purchases and subtract closing creditors (Accounts Payables) therefrom for computing the amount paid to suppliers.

(ii) Cash payment for operating expenses—Operating expenses are reported in the income statement on accrual basis. We need to adjust the operating expenses for outstanding expenses and prepaid expenses to ascertain cash payment for operating expenses.

(iii) Cash payment for income tax—The income statement indicates the provision made for income tax. The comparative balance sheet indicates the amount of tax payable in the beginning and at the end of the period. We can compute the cash payment for income tax as follows:

(iv) Payments for Interest—Though interest expense is subtracted from revenues to compute net income, according to Accounting Standard 3 cash flows arising from interest paid and interest/dividend received in cash of financial enterprise should be reported as cash flow from operating activities. In the case of other enterprises, cash flows from interest paid should be classified as financing activities and cash flows from interest and dividends received should be reported as cash flows from investing activities.

Indirect Method
In this method, net profit or loss is adjusted for the effects of transactions of a non-cash nature flow. In other words, Net profit or loss is adjusted for items which affected net profit but did not affect cash. As per AS-3, (Revised), under indirect method, net cash flow from operating activities is determined by adjusting net profit or loss for the effects of:

1. Non-cash items are to be added back. Non-cash items like
(a) Depreciation
(b) Goodwill written off
(c) Patents and Copyrights written off
(d) Appropriation to General Reserve
(e) Interim dividend
(f) Deferred taxes etc.

2. All other items for which the cash effects are investing or financing cash flows. The treatment of such items depend upon their nature. All investing and financing incomes are to be deducted from the amount of net profits while all such expenses are to be added back.

3. Changes in current assets and liabilities during the period. Increase in current assets and decrease in current liabilities are to be deducted while increase in current liabilities and decrease in current assets are to be added up.

Question 3.
Explain the major Cash Inflow and outflow from investing activities.
Answer:
Cash Flows from Investing Activities—Investing activities mean the acquisition and disposal of long-term assets and other investments not included in cash equivalent. Hence, investing activities include transactions that involve the purchase and sale of long-term assets like land, building, plant and machinery, etc, not held for resale and other investments.

The separate disclosure of cash flows arising from investing activities is significant because the cash flow represent the exent to which expenditures have been made for resources to generate future income and cash flows.

Examples of cash arising from investing activities are :
(a) Cash payments to acquire fixed assets (including intangibles). These payments include those relating to capitalised research and development costs and self-constructed fixed assets
(b) Cash receipts from disposal of fixed assets (including intangibles)
(c) Cash payments to acquires shares, warrants, or debt instruments of other enterprises and interests in joint ventures (other than payments for those instruments considered to be cash equivalents and those held for dealing or trading purposes)
(d) Cash receipts from disposal of shares, warrants, or debt instruments of other enterprises and interests in joint ventures (other than receipts from those instruments considered to be cash equivalents and those held for dealing or trading purposes)
(e) Cash advances and loans made to third parties (other than advances and loans made by a financial enterprises)
(f) Cash receipts from the repayment of advances and loans made to third parties (other than advances and loans of a financial enterprise)
(g) Cash payments for future contracts, forward contracts, option contracts, and swap contracts except when the contracts are held for dealing or trading purposes, or the payments are classified as financing activities; and
(h) Cash receipts from future contracts, forward contracts, option contracts, and swap contracts except when the contracts are held for dealing or trading purposes, or the receipts are classified as financing activities.

Question 4.
Explain the major Cash Inflows and outflows from financing activities.
Answer:
Cash Flows from Financing Activities—financing activities are activities that cause changes in the size and composition of capital and borrowings of the firm. The examples of cash flows arising from financing activities are
(a) Cash proceeds from issuing shares or similar other instruments;
(b) Cash proceeds from issuing debentures, loans, notes, bonds, and other short or long-term borrowings;
(c) Cash repayments of amount borrowed, and
(d) Payment of Dividend.

Special Items—AS-3 (Revised) provides for the treatment of certain special items as under :
(a) Foreign Currency Cash Flows—Cash flows arising from transactions in a foreign currency should be recorded in an enterprise’s reporting currency by applying to the foreign currency amount the exchange rate between the reporting currency and foreign currency at the date of cash flow. A rate that approximates actual rate may be used if the result is substantially the same as would arise if the rates at the date of cash flows were used. Unrealised gains and losses arising from changes in foreign exchange rate changes on cash and cash equivalent held or due in foreign currency is reported in the cash flow statement in order to reconcile cash and cash equivalents at the beginning and the end of the period.

(b) Extraordinary items—Cash flows associated with extraordinary items such as claims from insurance company, compnay’s winning a law suit or lottery, etc. should be classified as arising from operating, investing or financing activities and separately disclosed in cash flow statement.

(c) Interest and Dividends—Cash flow from interest and dividends received and paid should each be disclosed separately. Cash flows arising from interest paid and interest and dividends received in the case of a financial enterprise should be classified as cash flow arising from operating activities. In case of other enterprises, cash flows arising from interest paid should be classified as cash flows from financing activities while interest and dividends received should be classified as cash flows from investing activities. Dividends paid should be classified as cash flow from financing activities.

(d) Taxes on Income—Cash flows arising from taxes on income should be separately disclosed and should be classified as cash flows from operating activities unless they can be specifically identified with financing and investing activities.

(e) Acquisition and disposals of Subsidiaries and other Business Units—Tire aggregate cash flows arising from acquisition and from disposals of subsidiaries or other business units should be presented separately and classified as investing activities.

(f) Non-cash Transactions—Investing and financing transactions that do not require the use of cash or cash equivalents should be excluded from a cash flow statement. Such transactions should be disclosed elsewhere in the financial statements in a way that provides all the relevant information about these investing and financing activities. The exclusion of non-cash transactions from the cash flow statement is consistent with the objective of a cash flow statement as these do not involve cash flows in the current period. Examples of non¬cash transactions are :
(i) the acquisition of assets by assuming directly related liabilities;
(ii) the acquisition of an enterprise by means of issue of shares; and
(iii) the conversion of debt to equity.

Numerical Questions

Question 1.
Anand Ltd. arrived at a net income of Rs. 5,00,000 for the year ended March 31,2007. Depreciation for the year was Rs. 2,00,000. There was a gain of Rs. 50,000 on assets sold which was credited to profit and loss account. Bills Receivables increased during the year Rs. 40,000 and Bills Payables also increased by Rs. 60,000. Compute the cash flows operating activities by the indirect approach.
Answer:

Question 2.
From the information given below you are required to prepare the cash paid for the inventory :

Answer:

Question 3.
For each of the following transactions, calculate the resulting cash flow and state the nature of cash flow viz., operating, investing and financing.
(a) Acquired machinery for Rs. 2,50,000 paying 20% drawn and executing a bond for the balance payable.
(b) Paid Rs. 2,50,000 to acquire shares in Informa Tech, and received a dividend of Rs. 50,000 after acquisition.
(c) Sold machineary of original cost Rs. 2,00,000 with an accumulated depreciation of Rs. 1,60,000 for Rs. 60,000.
[Ans. Rs. 50,000 investing flow (out flow); Rs. 2,00,000 investing flow (outflow); Rs. 60,000 investing flow (outflow).]
Answer:

Question 4.
The following is the Profit and Loss Account of Yamuna Limited:

Additional Information:
(i) Trade debtors decrease by Rs. 30,000 during the year.
(ii) Prepaid expenses increase by Rs. 5,000 during the year.
(iii) Trade creditors decrease by Rs. 15,000 during the year.
(iv) Outstanding expenses increase by Rs. 3,000 during the year.
(v) Operating expenses included depreciation of Rs. 25,000. Compute net cash provided by operations for the year ended
March 31,2007 by the indirect method.
Answer:

Question 5.
Compute cash from operations from the following figures:
(i) Profit for the year 2005-06 is a sum of Rs. 10,000 after providing for depreciation of Rs. 2,000.
(ii) The current assets of the business for the year ended March 31,2006 and 2007 are as follows:

Answer:

Question 6.
From the following particulars of Bharat Gas Limited, calculate Cash Flows from Investing Activities. Also show the workings clearly preparing the ledger accounts.

Additional Information
1. Patents were written off to the extent of Rs. 40,000 and some Patents were sold at a profit of Rs. 20,000.
2. A Machine costing Rs. 1,40,000 (Depreciation provided thereon Rs. 60,000) was sold for Rs, 50,000. Depreciation charged during the year was Rs. 1,40,000.
3. On March 31, 2007, 10% Investments were purchased for
Rs. 1,80,000 and some Investments were sold at a profit of Rs. 20,000. Interest on Investment was received on March 31, 2007.
4. Amartax Ltd. paid Dividend @ 10% on its shares.
5. A plot of Land had been purchased for investment purposes and let out for commercial use and rent received Rs. 30,000.
Answer:

Question 7.
From the following Balance Sheet of Mohan Ltd. Prepare cash flow Statement:

Additional Information:
Machine Costing Rs. 80,000 on which accumulated depreciation
was Rs. 50,000 was sold for Rs. 20,000.
(Ans. : Cash flow from Operating Activity — Rs. 1,80,000
Cash flow from Investing Activity — Rs.(2,60,000)
Cash flow from Financing Activity — Rs. 20,000)
Answer:

Question 8.
From the following Balance Sheets of Tiger Super Steel Ltd., prepare Cash Flow Statement:
Answer:

Additional Information:
Depreciation Charge on Land & Building Rs. 20,000, and Plant Rs. 10,000 during the year.
(Ans.: Cash flow from Operating Activities — Rs. 34,800
Cash flow from Investing Activities — Rs. (50,400)
Cash flow from Financing Activities — Rs. 20,000)
Answer:

Question 9.
Prepare Cash Flow Statement from the following Information:

Additional Information:
Depreciation Charge on Plant amount of — Rs. 80,000.
(Ans.: Cash Inflow from Operating Activities Rs. 3,80,000 Cash Inflow from Investing Activities — Rs. (2,80,000)
Cash Inflow from Financing Activities — Rs. — NIL)
Answer:

Question 10.
From the following Information Prepare Cash flow Statements for Yogeta Ltd.

Additional Information:
Net Profit for the year After Charging Rs. 50,000 as Depreciation was Rs. 1,50,000. Dividend paid on Share was Rs. 50,000, Tax Provision created during the year amounted toRs. 60,000.
[Ans.: Cash from Operating Activities — Rs.-2,20,000
Cash from Investing Activities — Rs. (3,50,000)
Cash from Financing Activities — Rs. (80,000)]
Answer:

Question 11.
Following is the Financial Statement of Garima Ltd. Prepare Cash flow Statements.

Answer:
Cash Outflow (use) from Operating Activities Rs. (12,000)
Cash flow from Investing Activities Rs. (1,90,000)
Cash flow from Financing Activities Rs. (1,56,000).]

Question 12.
Following as the Balance Sheets of Computer India Ltd.:

Additional Information:
Interest paid on Debenture Rs. 600
[Ans.: Net Cash from Operating Activities — Rs. 2,100
Net Cash from Investing Activities — Rs. 1,000
Net Cash from Financing Activities — Rs.4,900]
Answer:

Detailed, Step-by-Step NCERT Solutions for 12 Accountancy Chapter 10 Accounting Ratios Questions and Answers were solved by Expert Teachers as per NCERT (CBSE) Book guidelines covering each topic in chapter to ensure complete preparation.

Accounting Ratios NCERT Solutions for Class 12 Accountancy Chapter 10

Accounting Ratios Questions and Answers Class 12 Accountancy Chapter 10

Test Your Understanding-I (Page No. 241)

State which of the following statements are True or False :

(a) The only purpose of financial reporting is to keep the managers informed about the progress of operations.
(b) Analyses of data provided in the financial statements as is termed as financial analysis.
(c) Long-term creditors are concerned about the ability of a firm to discharge its obligations to pay interest and repay the principal amount of term.
(d) A ratio is always expressed as a quotient of one number divided by another
(e) Ratios help in comparisons of a firm’s results over a number of accounting periods as well as with other business enterprises.
(f) One ratio reflect both quantitative and qualitative aspects.
Answer:
(a) False
(b) True
(c) True
(d) False
(e) True
(f) False.

On Test Your Understanding-II (Page No. 255)

Question 1.
The following groups of ratios primarily measure risk—
(a) liquidity, activity, and profitability
(b) liquidity, activity and common stock
(c) liquidity, activity and debt
(d) activity, debt and profitability
Answer:
(d) activity, debt and profitability

Question 2.
The ratios are primarily measures of return.
(a) liquidity
(b) activity
(c) debt
(d) profitability
Answer:
(b) activity

Question 3.
The of a business firm is measured by its ability to satisfy its short-term obligations as they come due.
(a) activity
(b) liquidity
(c) debt
(d) profitability
Answer:
(b) liquidity

Question 4
ratios are a measure of the speed with which various accounts are converted into sales or cash.
(a) Activity
(b) Liquidity
(c) Debt
(d) Profitability
Answer:
(a) Activity

Question 5.
The two basic measures of liquidity are
(a) inventory turnover and current ratio
(b) current ratio and liquid ratio
(c) gross profit margin and operating ratio
(d) current ratio and average collection period
Answer:
(b) current ratio and liquid ratio.

Question 6.
The is a measure of liquidity which excludes generally the least liquid asset.
(a) current ratio, accounts debtors
(b) liquid ratio, accounts debtors
(c) current ratio, inventory
(d) liquid ratio, inventory
Answer:
(d) liquid ratio, inventory.

Test Your Understanding-III (Page No. 262)

Question 1.
The ……….. is useful in evaluating credit and collection policies.
(a) average payment period
(b) current ratio
(c) average collection period
(d) current asset turnover
Answer:
(c) average collection period

Question 2.
The measures the activity of a firm’s inventory.
(a) average collection period
(b) inventory turnover
(c) liquid ratio
(d) current ratio
Answer:
(b) inventory turnover

Question 3.
The ratio may indicate the firm is experiencing stock outs and last sales.
(a) average payment period
(b) inventory turnover
(c) average collection period
(d) quick
Answer:
(a) average payment period

Question 4.
ABC Co. extends credit terms of 45 days to its customers. Its credit collection would be considered poor if its average collection period was …….
(a) 30 days
(b) 36 days
(c) 47 days
(d) 57 days
Answer:
(c) 47 days

Question 5.
………… are especially interested in the average payment period, since it provides them with a sense of the bill-paying patterns of the firm.
(a) Customers
(b) Stockholders
(c) Lenders and suppliers
(d) Borrowers and buyers
Answer:
(c) Lenders and suppliers

Question 6.
The ………… ratios provide the information critical to the long-run operation of the firm.
(a) liquidity
(b) activity
(c) solvency
(d) profitability
Answer:
(c) solvency

Do it Yourself (Page No. 247)

Question 1.
Current ratio = 4.5 :1, quick ratio = 3:1. Inventory is Rs. 36,000. Calculate the current assets and current liabilities.
Answer:

Question 2.
Current liabilities of a company are Rs. 5,60,000, current ratio is 5:2 and quick ratio is 2 :1. Find the value of the stock.
Answer:

Question 3.
Current assets of a company are Rs. 5,00,000. Current ratio is 2.5 : 1 and quick ratio is 1 : 1. Calculate the value of current liabilities, liquid assets and stock.
Answer:

Do it Yourself (Page No. 257)

Question 1.
Calculate the amount of gross profit:
Average stock = Rs. 80,000
Stock turnover ratio = 6 times
Selling price = 25% above cost
Answer:

Question 2.
Calculate Stock Turnover Ratio :
Annual sales = Rs. 2,00,000
Gross Profit = 20% on cost of Goods Sold
Opening stock = Rs. 38,500
Closing Stock = Rs. 41,500
Answer:

Short Answer Type Questions

Question 1.
What do you mean by Ratio Analysis?
Answer:
Ratio Analysis: The English word ratio comes directly from Latin. The Latin word has many derivates in the English language, among them are reason/ratio, rational and relational. Ratio is defined formally as “the indicated quotient of two mathematical expressions”— and indeed, a ratio does result from the division of one number into another—and as “the relationship between two or more things”.

An operational definition of a financial ratio is the relationship between two financial values. The word “relationship” implies that a financial ratio is the result of comparing mathematically two values.

And this numerical comparison is important, for these ratios are used as indexes, and as indexes, they are used to make qualitative judgements about the financial health of the firm.

Analysis of the firm by financial ratios enables the financial manager as well as interested external parties, to evaluate the firm’s financial performance and condition rapidly by making comparisons of ratios obtained from the firm with ratios obtained from comparable firms. Financial ratio also presents ready comparison of firm’s financial performance and condition over time as a way of identifying and evaluating performance trends.

Ratio analysis requires considerable judgement and direction by the analyst if it is to serve as a basis for future financial and operating decisions. Rule of thumb and other mechanical interpretations may produce disastrous decisions by those who are ill-informed about the ambiguity of information that may be contained in ratios.

Financial and operating relationships expressed in terms of ratios or otherwise have little significance except as they are judged on the basis of appropriate standards of comparison. Therefore, in interpreting the ratios of a particular business, the analyst cannot determine whether the ratios of a particular business indicates favourable or unfavourable conditions unless there are available measuring devices standards of comparison may consist of

• Mental standard of the analyst i.e., general conception of what is adequate or normal which has been gained by his personal experience and observation.
• Ratios and percentages based on the records of the past financial and operating performance of the individual business.
• Ratios and percentages of selected competing companies, especially the most progressive and successful ones.
• Ratios and percentages developed by using the data included in the current budgets.
  Such ratios would be based on the individual company’s past experience modified by anticipated changes during the accounting period. These ratios would properly be called “good ratios”.
• Ratio and percentages of the industry of which the individual company is a member.

Question 2.
What are various types of ratios?
Answer:
Ratios can be classified from various points of view. In reality, the classification depends on the objectives and available data. Thus, accounting ratio may be classified as under :
(i) Traditional Classification
(ii) Functional Classification
(i) Traditional Classification : Traditional classification of accounting ratios is based on the statement from which the ratios are calculated. Ratios may be based on figures in the balance sheet, in the profit and loss account or in both. On this basis the various types of accounting ratios are as follows :

(a) Balance Sheet Ratios: In case both variables are from balance sheet, it is classified as Balance Sheet Ratios. For example ratio of current assets to current liabilities known as current ratio is calculated using both figures from Balance Sheet. Some other ratios are following which comes under this category :

• Current Ratio
• Quick Ratio
• Debt Equity Ratio
• Proprietary Ratio

(b) Income Statement Ratios : A ratio of two variables from the Income Statement (Profit and Loss A/c) is known as Income Statement Ratio. For example ratio of Gross Profit to Sales known as Gross Profit Ratio is calculated using both figures from the income statement. Some other ratios are :

• Gross Profit Ratio
• Net Profit Ratio
• Operating Ratio
• Stock Turnover Ratio

(c) Composite or Inter-Statement Ratios : If a ratio is computed with one variable from Income Statement and another variables from Balance Sheet, it is called composite ratio. For example, ratio of credit sales to debtors and bills receivable known as debtors turnover ratio is calculated using one figure from income statement (credit sale) and another figure from balance sheet (Debtors and Bills receivable). Some other ratios are :

• Return on Investment
• Return on Equity
• Fixed Assets Turnover Ratio
• Debtors Turnover Ratio
• Creditors Turnover Ratio

(ii) Functional Classification : The most popular and useful classification of ratios is the functional classification. Functional classification is the classification of ratios according to functions. Accounting ratios are classified as under :

(a) Liquidity Ratios: It measures the short term solvency i.e. the firm ability to pay its current dues. The term liquidity means the conversion of the assets into cash without much loss. The objective is to find the ability of the business enterprise to meet short term liabilities. The ratios included in this category are :

• Current Ratio
• Liquid Ratio

(b) Solvency Ratios : These ratios are computed to judge the ability of a firm to pay off its long-term liabilities. It shows the proportion of the fund which is provided by outside creditors in comparison to owners. These ratios shown the long term financial solvency and measures the enterprise’s, ability to pay the interest regularly and of repay the principal on maturity or in pre-determined installments at due dates. The following ratios are normally computed for solvency analysis:

• Debt Equity Ratio
• Total Assets to Debt Ratio
• Proprietary Ratio
• Interest Coverage Ratio

(c) Activity (or Turnover) Ratios : Activity ratios are used to indicate the efficiency with which assets such as stock, debtors, fixed assets etc. of the firm are being utilised. These ratios are also known as Turnover Ratios because they indicate the speed with which assets are being converted or turned over into sales. These ratios, thus express the relationship between cost of goods sold or sales various assets and arte expressed in number of times. The following are the important ratios of this category:

• Stock Turnover Ratio
• Debtors Turnover Ratio
• Creditors Turnover Ratio
• Working Capital Turnover Ratio
• Fixed Assets Turnover Ratio
• Current Assets Turnover Ratio

(d) Profitability Ratios : Efficiency of a business is measured in term of profits. Thus profitability ratio are computed to measures the efficiency of a business. Profit earning capacity may be expressed in the form of sales. Some important profitability ratios are :

• Gross Profit Ratio
• Operating Ratio
• Net Profit Ratio
• Return on Investment Ratio
• Earning Per Share Ratio
• Dividend Per Share Ratio

Question 3.
What relationship will be established to study:
(a) Inventory Turnover
(b) Debtors Turnover
(c) Payable Turnover
(d) Working Capital Turnover
Answer:
These all four ratios are Turnover or Activity Ratios. These ratios measures the effectiveness with which a firm uses its available resources. These ratios are called ‘Turnover Ratios’ since they indicate the speed with which the resources are being turned into sales. These ratios, thus express the relationship between cost of goods sold or sales and various assets and are expressed in number of times.

(a) Inventory Turnover: This is also called Stock Turnover Ratio. This ratio establishes a relationship between cost of goods sold and average inventory. The objective of computing this ratio is to determine the efficiency with which the inventory is utilised.

This ratio shows the rate at which stocks are converted into sales. The higher the ratio, the better it is for the business, since it means that stock is being quickly converted into sales. Industries which has very high stock turnover ratio may be operating with low margin of profits and vice-versa.

(b) Debtors Turnover Ratio: This ratio is computed to establishes the relationship between net credit sales and average debtors (or receivable) of the year. It shows the rate at which cash is generated by the turnover ratio of debtors.

This ratio indicates the number of times the receivable are turned over in a year in relations to sales. It shows how quickly debtors are converted into cash. The higher the ratio, the better it is, since it means speedier collection and lesser amount being blocked up in debtors and vice versa.

(c) Payable Turnover Ratio : It is also called Creditors Turnover Ratio. It indicates the pattern of payment of accounts payable. An accounts payable arise on account of credit purchase, it expresses relationship between credit purchases and accounts payable.

It shows average payment period. By comparing it with the credit period allowed by the suppliers,-conclusion may be drawn. Lower ratio means credit allowed by the supplier is not enjoyed by the business. Higher ratio means delayed payment to supplier which is not a very good policy as it may affect the reputation of the business.

(d) Working Capital Turnover: This ratio indicates whether the working capital has been effectively utilized or not in making sales. In fact, in the short run, it is the current assets and current liabilities which plays a major role. A careful handling of current assets and current liabilities will mean a reduction in the amount of capital employed thereby improving turnover.

Working Capital Turnover Ratio \(=\frac{\text { Net Sales }}{\text { Working Capital }}\)
A high working capital turnover ratio show the efficient utilisation of working capital in generating sales. A low ratio, on the other hand, may indicate excess of working capital or has not been utilized efficiently.

Question 4.
Why would the Inventory Turnover Ratio be more important wrhen analysing a grocery store than an insurance company?
Answer:
Inventory turnover is more important for a grocery store being a trading concern rather than insurance company, contracting for indemnity. Inventory is an element of current assets.

Inventory is needed for smooth flow of production and sales inventory is of three types i.e. raw material, work-in-progress and finished goods. Raw- material and work-in-progress inventory is maintained for the uninterrupted flow of production. Finished goods inventory is kept for meeting the demands of customers.

Inventory turnover ratio measures the efficiency with which inventory has been converted into sales. Inventory is generally valued at cost.

This ratio indicates the speed with which the goods have been sold. Low ratio means low speed of sales and high ratio indicates that goods have not been retained in the godown for a longer period. Higher ratio is considered good from the view point of liquidity.

Question 5.
The liquidity of a business firm is measured by its ability to satisfy its long term obligations as they come due. Comment.
Answer:
The term solvency means the ability of the enterprise to meet its obligations on the due date. Some payments have short-term maturity and some have long term maturity. Long-term liquidity means ability to meet long term commitments or obligations, long term lenders are primarily interested in this type of analysis.

Leverage or Capital Structure Ratio : Solvency of business is related to its debt paying capacity. Normally, the ordinary shareholders, debenture holders, financial institutions and other long term creditors are interested in these ratios. With the help of these ratios, long term creditors can analysis the capacity of business to pay interest and the principal. Therefore, long term solvency of business means its ability to pay the long term debts and interest thereon regularly.

Therefore, the long term solvency or financial position has two aspects—
(i) The ability to repay principal on due date.
(ii) The ability to pay interest regularly.

(i) Debt-Equity Ratio – In any business, there should be equitable balance between owned capital and debt capital because it affects long term solvency of business. If a business procures more funds from the owners of business, it will secure the interest of creditors.

(ii) Proprietary Ratio – This ratio is another form of debt equity ratio. It is also known as Net Worth to Total Assets Ratio. This ratio establishes relationship between shareholders’ funds and total assets of business.

The higher ratio, the more profitable it is for the creditors. If the ratio is low, the creditors can be suspicious about the repayment of their debt on liquidation of company.

Coverage Ratio – To evaluate the long term solvency, coverage ratios are calculated. In the ordinary course of business, the claims of creditors are’ not met by selling the fixed assets. Rather, these claims are paid out of income of the firm. If the firm is able to pay these claims in time, the finanacial position of the firm will be considered sound. The coverage ratio includes

(i) Interest Coverage Ratio—With the help of this ratio, it can be ascertained whether the interest on long term debts of business can be paid out of profits or not. The higher the ratio, the safer will be the interests of creditors.
Interest Coverage Ratio =\(\frac{\text { EBIT }}{\text { Interest }}\)
EBIT = Earning before Interest and Taxes.

(ii) Dividend Coverage Ratio—This ratio measures the dividend paying capacity of the firm.
Dividend Coverage Ratio = \(\frac{\text { Earnings after Taxes }}{\text { Preference Dividend }}\)

(iii) Fixed Charges Coverage Ratio—This ratio considers both interest on long term loans and dividend on preference share capital.
Fixed Charge Coverage Ratio = \(\frac{\text { EBIT }}{\text { Interest + Preference Dividend }}\)

Question 6.
The average age of inventory is viewed as the average length of time inventory held by the firm or as the average number of days sales in inventory. Explain.
Answer:
Inventory is an element of current assets. Inventory is needed for smooth flow of production and sales. Inventory is of three types i.e., raw-material, work-in-progess and finished goods. Raw-material and work-in-progress inventory is maintained for the uninterupted flow of production.

Finished goods inventory is kept for meeting the demands of customers. The firms usually maintain finished goods inventory. Inventory is generally valued at cost. Firstly, to calculate inventory turnover ratio and then convert it into number of days for the calculation of average age of inventory.

If the Inventory Turnover ratio goes up, the average age of inventory will go down and vice versa.

Aging Schedule of Inventory—According to the time, Inventory can be calculated and classified to find out those items which are used in the production process at a slow rate or which are sold at slow rate. By preparing aging schedule of Inventory, the dates of their purchase or manufacture are taken note of. A specimen of aging schedule of inventory is as under :

From the above table, it is clear that 50% of total inventory is in stocks for more than 80 days.

Long Answer Type Questions

Question 1.
Who are the users of financial ratio analysis? Explain the significance of ratio analysis to them?
Answer:
The following are the main users of financial ratio analysis.
1. Investors and Owners
2. Management
3. Short Term Creditors
4. Long Term Creditors
Tire significance of ratio analysis for the various groups may be discussed as under:
1. Investors and Owners : Investors and Owners are primarily interested in the Profitability and safety of their investments. Hence they calculate profitability ratios such as earning per share, dividend per share, return on investment, return on equity, dividend yielded etc. On the basis of these ratios, investors.decide whether to buy or retain the shares of the company.

2. Management: Management makes the use of ratio analysis as a means of self-evaluation. Management assesses its managerial skill and performance on the basis of profitability ratios and turnover ratios. Management uses different ratios for forecasting to events. Management can assess its performance by making inter-firm comparison and intra-firm comparison.

3. Short Term Creditors : Short term creditors like suppliers of goods and lenders supplying short term loans, uses liquidity ratio such as current ratio and acid test ratio to assess the liquidity position of the company. Liquidity ratios give them an idea of company’s ability to repay their claims at the time of maturity of the claims.

4. Long Term Creditors : Long term creditors are the creditors who provide funds to the company for a period over one year. Long term creditors are interested in the solvency of the company and the company’s ability of pay its interest obligations. Solvency ratios such as debt equity ratio, proprietary ratio and interest coverage ratio are calculated by long term creditors.

Question 2.
What are liquidity ratios? Discuss the importance of current and liquid ratio.
Answer:
Liquidity Ratios : It measures the short term solvency i.e. the firm’s ability to pay its current dues. The term liquidity means the conversion of the assets into cash without much loss. The objective is to find out the ability of the business enterprise to meet short term liabilities. The ratios included in this category are :
(i) Current Ratio
(ii) Liquid Ratio

(i) Current Ratio: Current ratio is the proportion of current assets to current liabilities.
\(\text { Current Ratio }=\frac{\text { Current Assets }}{\text { Current Liabilities }}\)
Current assets which means the assets which are held for their conversion into cash with in a year. The following are the examples of current assets:

Cash Balances – Accurred Income
Bank Balances – Marketable Securities
Debtors – Bills Receivable
Stock – Prepaid Expenses etc.
Short term loans

Current Liabilities which mean the liabilities which are expected to be matured within a year. The following are the example of current liabilities:

Creditors – Provision for Tax
Bank Overdraft – Unclaimed dividend
Bills Payable – Income received in advance etc.
Short Term Loans

Importance : An ideal ratio is 2 :1. A higher ratio indicates poor investment policies of the management and poor inventory control while a low ratio indicates lack of liquidity and shortage of working capital. The current ratio, thus, throws a good light on the short term financial position and policy of a firm.

(ii) Liquid Ratio or Quick Ratio: It is the ratio of quick (or liquid) assets to current liabilities.
\(\text { Quick Ratio }=\frac{\text { Quick Assets }}{\text { Current Liabilities }}\)
Quick Assets (or liquid Assets) = Current Assets – Stock – Prepaid expenses.

The objectives of computing this ratio is to measures the ability of the firm to meet its short term obligation as and when due without relying upon the realization of stock.

Importance : A quick (or liquid) ratio of 1 : 1 is supposed to be good for the reason that it indicates availability of funds to meet the liabilities 100%. If this ratio is more than 1 : 1 it can be said that the financial position of the business enterprise is sound and good.

On the other hand. If the ratio is less than 1 :1 i.e. liquid assets are less than current liabilities the financial position of the concern shall be deemed to be unsound and additional cash will have to be provided for the payment of current liabilities.

Question 3.
How would you study the solvency position of a firm?
Answer:
Solvency position of a firm may be studied with the help of solvency ratios. These solvency or leverage ratios are important to creditors, since they reflect the capacity of firm’s revenue to support interest and other fixed charges, and whether there are sufficient assets to pay-off the debt in the event of liquidation.

Shareholders, are concerned with leverage, since interest payments increases with greater debt. If borrowing and interest are excessive, the company can even experience bankruptcy.

(i) Total Debt to Total Assets Ratio—The ratio of total debt to total assets, generally, called the debt ratio, measures the percentage total funds provided by creditors. Debts includes current liabilities and all creditors, moderate debt ratio, since the lower the ratio, the greater the cushion against creditors losses in the event of liquidation. In contrast to the creditors preference of low debt ratios the owners may seek high leverage either.
(i) to magnify earnings or
(ii) because raising new equity means giving up some degree of control. If the debt ratio is too high, there is a degree of encouraging irresponsibility on the part of the owners.

The stake of the owners can become so small that speculative activity, if it is successful, will yield a substantial return to the owners. If the venture is unsuccessful, however, only a concrete loss is incurred by the Owners because there investment is small.

(ii) Capitalisation Ratio : Another widely used measure of financial or solvency position is the capitalisation ratio, which is derived by dividing long-term debt by the total of long-term debt plus owner’s equity. Since the sum of debt and owner’s equity represents the permanent capital of the firm, this ratio indicates the portion of the permanent capital that is financed with debt.

(iii) Earning Coverage Ratio—This in many ways a superior measure of financial risk to the leverage ratio as it attempts to measure the company’s ability to avoid future financial difficulties which can arise because of its use of debt finance. The larger this ratio, the greater the reduction of the company’s earnings which can occur before the company will default on its interest payments.

EBIT = Earnings before Interest & Taxes.

(iv) Ratio of Owner’s-Equity to Total Assets—The ratio of owner’s equity to total assets shows the percentage of the total investment. This ratio often called the “Proprietary ratio” or Shareholder Equity Ratio.

The larger amount of owner’s equity indicates an improvement in the long term financial position, since there is relatively greater margin of safely for outside creditors and less long-term pressure from the point of view of the owners. The most conservative, although not always the most profitable, basis of financing when broad or other long term obligations are used in place of capital stock is to provide for the gradual retirement of the debt.

From the point of view of creditors, the larger the percentage of assets that is supplied by shareholders, the more satisfactory the fianancial structure of the business. Since owner’s equity is a “Cushion” that first absorbs losses.

However, an upward trend in this ratio is usually considered by creditors to be favourable, and the larger the percentage of funds, supplied by outside creditors, the less ‘conservative’ the financial structure is likely to be especially in periods of poor business, because of the fixed interest and necessity of paying or refunding maturing debts.

Question 4.
What are important profitability ratios? How are they worked cut?
Answer:
Efficiency of a business is measured in terms of profits. Thus profitability ratio are computed to measure the efficiency of a business. Profit earning capacity may be expressed in the form of sales. Some important profitability ratios are :
(i) Gross Profit Ratio
(ii) Operating Ratio
(iii) Operating Profit Ratio
(iv) Net Profit Ratio
(v) Overall Profitability Ratio
(vi) Return of Shareholder fund
(vii) Return on Capital Employed etc.

(i) Gross Profit Ratio: The main objective of computing tl us ratio is to be determine the efficiency with which production and/or purchase operations are carried on. It establishes relationship of gross profit on sales of a firm, which is calculated

Gross Profit = Net Sales – Cost of Goods Sold
Cost of Goods Sold = Opening Stock + Purchases + Direct Expenses – Closing Stock
Net Sales = Total Sales – Sales Return

(ii) Operating Ratio : This ratio establishes the relationship between the cost of goods sold plus other operating expenses to net sales. The lower the percentage of operating ratio, the higher the net profit ratio.


Operating Expenses = Office and Financial Expenses + Administrative Expenses + Selling and Distribution Expenses + Discount + Bad Debts + Interest on Short Term Loans Cost of Goods Sold = Sales – Gross Profit

(iii) Operating Profit Ratio : It is calculated to reveal operating margin. It may be computed directly or as a residual of operating ratio.
Operating Profit Ratio = 100 – Operating Ratio Alternatively,

(iv) Net Profit Ratio : Net profit ratio is based on all inclusive concept of profit JH: relates sales to net profit after operational as well as non-operational expenses and income
\(\text { Net Profit Ratio }=\frac{\text { Net Profit }}{\text { Sales }} \times 100\)
Net Profit is taken after income tax.

(v) Overall Profitability Ratio : The Overall Profitability Ratio establishes the relationship of profit to the amount of funds employed.
\(\text { Overall Profitability Ratio }=\frac{\text { Profit }}{\text { Investment of Funds }} \times 100\)

(vi) Return of Shareholder’s fund: This ratio reflects the return on shareholder’s fund that the business enterprise was able to earn. Return on Shareholder’s Fund =

(vii) Return on Equity Shareholders’ fund : It is computed to draw an idea about the return available to equity shareholders.

Profit after appropriation less Preference dividend

(viii) Return on Capital Employed or Investment (ROCE or ROI): This ratio, also known as return on investment, is a basic ratio of profitability. It is calculated by establishing a relationship between the profit earned and the capital employed to earn the profit. It is therefore an indicator of the earning capacity of the capital invested in the business.

Return on Capital Employed
Capital Employed = Fixed Assets + Working Capital = Long Term Funds + Share Capital + Reserves and Surplus – Ficitious Assets (Miscellaneous Expenditure)

Question 5.
Financial ratio analysis are conducted by four groups of analysis : Managers, equity investors, long term creditors and short term creditors. What is the primary emphasis of each of these groups in evaluating ratios?
Answer:
Financial ratio analysis are conduced by four groups of analysis : Managers, equity investors, long term creditors and short term creditors. The primary emphasis of each these groups in evaluating ratios are following

(i) Managers : Manager’s makes the use of ratio analysis as a means of self evaluations. Managers assesses their managerial skill and performance on the basis of profitability ratios and turnover ratio. They uses different ratios for forecasting of events. They can assess their performance by making inter-firm comparison and intra-firm comparison.

(ii) Equity Investors : They are primarily interested in the profitability and safety of their investments. Hence they calculate profitability ratios such as earning per share, dividend per share, return on investment, return on equity, divided yield etc. On the basis of these ratios, investors decide whether to buy or retain the share of the company.

(iii) Long Term Creditors: Long term creditors are the creditors who provide funds to the company for a period over one year. Long term creditors are interested in the solvency of the company and the company’s ability to pay its interest obligations. Solvency ratios such as debt equity ratio, proprietary ratio and interest coverage ratio are calculated by long term creditors.

(iv) Short Term Creditors: Short Term creditors like suppliers of goods and lenders supplying short term loans, uses liquidity ratios such as current ratio and acid test ratio to assess the liquidity position of the company. Liquidity ratios give them an idea of company’s ability to repay their claims at the time of maturity of the claims.

Question 6.
The current ratio provides a better measure of overall liquidity only when a firm’s inventory cannot easily be converted into cash. If inventory is liquid, the quick (liquid) ratio is a preferred measure of overall liquidity. Explain.
Answer:
(i) Current Ratio : This ratio establishes the relationship between current assets and current liabilities. With its help, the ability of the business to pay-off its short-term liabilities is determined. It helps to find out how many times current assets are there in business as compared to current liabilities. This ratio is calculated by dividing current assets by current liabilities. Current ratio of 2 :1 is considered ideal i.e. The current assets should be twice the current liabilities.
\(\text { Current Ratio }=\frac{\text { Current Assets }}{\text { Current Liabilities }}\)
Current assets are those assets which are converted into cash within one year or an operating cycle. They include cash in hand, bank balance, stock, debtors, prepaid expenses, bills receivable, short-term investments etc. Current Liabilities are those liabilities which have to be paid during one year.

These include, creditors, bills payable, outstanding expenses, dividend payable, short-term loans, bank overdrafts etc. This ratio is also called Working Capital Ratio. Because working capital is the difference between current assets and current liabilities.

This ratio gives us the information as to whether the business has adequate current assets to pay-off its current liabilities. Current assets should be more than current liabilities so that despite fall in their prices, current liabilities could be paid easily. If current ratio is 2 :1, it means that the current liabilities would be paid even if there is 50% fall in the prices of current assets.

The greater this ratio, better will be the short term solvency of the firm and more safe will be the interests of the short term creditors.

This ratio should neither be too high nor too low. High ratio is an indicator of weak investment policy of the firm and low ratio increases the risk in payment of short term debts. High ratio also means that funds of the firm are lying surplus and unutilised.

Although, the current ratio should be 2 :1 but it is not a fixed or certain rule because it depends on the nature of business, its working conditions and availableHinancial resources.

For public utility companies, a current ratio of less than 2 : 1 may also be satisfactory because in such business, the amount of current assets is normally low. Contrarily, for a wholesaler who purchases goods on cash or on credit of small period and sells on credit to the retailers, the current ratio should be high.

Current Ratio’s main limitation is that is a quantitative measure, not a qualitative one. To ascertain this ratio, all current assets are given equal importance. In other words, the liquidity of individual current asset is given no attention. But there is difference in the liquidity of various current assets.

Cash is the most liquid asset. On the other hand, stock is the least liquid of all current assets. Debtors, B/Rs etc. are more liquid as compared to stock but less liquid than cash. The current ratio of two firms can be similar. But if the current assets of a firm consist of stock as a major proportion, it will be less liquid as compared to other firm.

This ratio can be easily altered for window dressing. Window dressing means manipulation in current assets and current liabilities to show favourable position as compared to the actual one.

This manipulation is done by higher valuation the stock, lesser provision for bad and doubtful debts, lesser amount of provisions and transferring a current liability to a long term liability. All this will raise the Current Ratio. Therefore, the current ratio can’t be an absolute measure of short term solvency of the firm.

(ii) Liquidity Ratio or Acid Test Ratio or Quick Ratio—With the help of this ratio, the capacity of the firm to pay off its current liabilities immediately is measured. This ratio is calculated by dividing liquid assets by current liabilities.
Liquid assets are those assets which can immediately or in a short period be converted into cash without much loss Liquid assets do not include stock and prepaid expenses because stock is less liquid and its price fluctuates. Prepaid expenses can’t be realised

A liquid ratio of 1 :1 is considered as standard ratio. The higher this ratio, more will be the short term solvency of the business. This ratio is calculated to remove the shortcomings of the current ratio. Tins ratio is considered better than current ratio. Sometimes, the current ratio is high because of large proportion of stock but due to low liquidity ratio, the short term financial position of business is weak.

If liquid assets are less than current liabilities, the management should manage cash. According to some authors to calculate this ratio, liquid liabilities should be used in place of current liabilities. Liquid liabilities are those liabilities which are to be paid in near future. Bank overdraft and cash credit are not included in them because they are not immediately payable.
\(\text { Liquidity Ratio }=\frac{\text { Liquid Assets }}{\text { Liquid Liabilities }}\)

Although liquid ratio is considered better than current ratio, but to analysis short term financial position of the business both ratios should be used simultaneously.

Numerical Questions

Question 1.
Following is the Balance Sheet of Rohit and Co. as on March 31, 2006.

Calcuate Current Ratio
(Ans. Current Ratio 2:1)
Answer:

Question 2.
Following is the Balance Sheet of Title Machine Ltd. as on March 31, 2006.

Calculate Current Ratio and Liquid Ratio.
(Ans. Currcnt Ratio 0.8, Liquid Ratio 0.37: 1)
Answer:

Question 3.
Current Ratio is 3 : 5. Working Capital is Rs. 90,000. Calculate the amount of Current Assets and Current Liabilities.
(Ans. Current Assets Rs. 1,26, 000 and Current Liabilities Rs. 36,000)
Answer:

Question 4.
Shine Limited has a current ratio 4.5 :1 and quick ratio 3 : 1; If the stock is 36,000, calculate current liabilities and current assets. (Ans. Current Assets Rs. 1,08,000, current liabilities Rs. 24,000)
Answer:

Question 5.
Current liabilities of a company are Rs. 75,000. If current ratio is 4:1 and liquid ratio is 1:1, calculate value of current assets, liquid assets and stock. (Ans : Current Assets Rs. 3,00,000. Liquid Assets Rs. 75,000 and stock Rs. 2,25,000
Answer:

Question 6.
Handa Ltd. has stock of Rs. 20,000. Total liquid assets are Rs. 1,00,000 and quick ratio is 2 :1. Calculate current ratio. (Ans : Current Ration 2.4 :1)
Answer:

Question 7.
Calculate debt equity ratio from the following information:
Total Assets – Rs. 15,00,000
Current Liabilities – Rs. 6,00,000
Total Debts – Rs. 1200,000
(Ans : Debt Equity Ratio 2 : 1)
Answer:

Question 8.
Calculate Current Ratio if: Stock is Rs. 6,00,000; Liquid Assets Rs. 24,00,000; Quick Ratio (Ans. Current Ratio 2.5 :1)
Answer:

Question 9.
Compute Stock Turnover Ratio from the following information:
Net Sales – Rs. 2,00,000
Gross Profit – Rs. 50,000
Closing Stock – Rs, 60,000
Excess of Closiiig Stock – Rs. 20,000
over Opening Stuck
(Ans : Stock Turnover Rho 3 times)
Answer:

Question 10.
Calculate following ratios from the following information:
(i) Current ratio
(ii) Acid test ratio
(iii) Operating Ratio
(iv) Gross Profit Ratio
Current Assets – Rs. 35,000
Current Liabilities – Rs. 17,500
Stock – Rs. 15,000
Ope rating Expences – Rs. 20,000
Sales – Rs. 60,000
Cost of Goods Sold – Rs. 30,000
(Ans: Current Ratio 2:1; Liquid Ratio 1.14: 1; Operating Ratio
83.3%: Gross Profit Ratio 50%)
Answer:

Question 11.
From the following information calculate :
(i) Gross Profit Ratio
(ii) Inventory Turnover Ratio
(iii) Current Ratio
(iv) Liquid Ratio
(v) Net Profit Ratio
(vi) Working capital Ratio :

(Ans: Gross Profit Ratio 23.81; Inventory Turnover Ratio 2.4 times; Current Ratio 2.6 : 1; Liquid Ratio 1.27 : 1; Net Profit Ratio 14.21%; forking Capital Ratio 2.625 times)
Answer:

Question 12.
Compute Gross Profit Ratio, Working Capital Turnover Ratio, Debt Equity Ratio and Proprietary Ratio from the following information:

(Ans : Gross Profit Ratio 40%; Working Capital Ratio 8.33 times; Debt Equity Ratio 2:5; Proprietary Ratio 25:49)
Answer:

Question 13.
Calculate Stock Turnover Ratio if :
Opening Stock is Rs. 76,250, Closing Stock is 98,500, Sales is Rs. 5,20,000, Sales Return is Rs. 20,000, Purchases is Rs. 3,22,250. (Ans : Stock Turnover Ratio 3.43 times)
Answer:

Question 14.
Calculate Stock Turnover Ratio from the data given 1 below:

Answer:

Question 15.
A trading firm’s average stock is Rs. 20,000 (cost). If the stock turnover ratio is 8 times and the firm sells goods at a profit of 20% on sale, ascertain the profit of the firm. (Ans : Profit Rs. 40,000)
Answer:

Profit = Sales – Cost of Goods Sold
= Rs. 2,00,000 – Rs. 1,60,000
= Rs. 4,000

Question 16.
You are able to collect the following information about a company for two years :

Calculate Stock Turnover Ratio and Debtor Turnover Ratio if in the year 2004 stock in trade increased by Rs. 2,00,000
(Ans. Stock Turnover Ratio 2.4 times, Debtors Turnover Ratio 4.52 times)
Answer:

Question 17.
The following Balance Sheet and other information, calculate following ratios:
(i) Debt Equity Ratio
(ii) Working Capital Turnover Ratio
(iii) Debtors Turnover Ratio.

(Ans : Debt Equity 12 :19; Working Capital Turnover 1.4 times; Debtors Turnover 2 times)
Answer:

Question 18.
The following is the summerised Profit and Loss account and the Balance Sheet of Nigam Limited for the year ended March 31, 2007:

Answer:
Calculate (i) Quick Ratio
(ii) Stock Turnover Ratio
(iii) Return on Investment
(Ans: Quick Ratio 7:13; Stock Turnover Ratio 3.74 times; Return on Investment 41.17%) .
Answer:

Question 19.
From the following, calculate
(a) Debt Equity Ratio
(b) Total Assets to Debt Ratio
(c) Proprietary Ratio.

Answer:

Question 20.
Cost of Goods Sold is Rs. 1,50,000. Operating expenses are Rs. 60,000, Sales is Rs. 2,60,000 and Sales Return is Rs. 10,000. Calculate Operating Ratio.
(Ans. Operating Ratio 84%)
Operating Ratio
Answer:

Question 21.
The following is the summerised transactions and Profit and Loss Account for the year ending March 31,2007 and the Balance Sheet as on that date.


Calculate (i) Gross Profit Ratio, (ii) Current Ratio, (iii) Acid Test Ratio, (iv) Stock Turnover Ratio, (v) Fixed Assets Turnover Ratio.
(Ans : Gross Profit Ratio 50%; (ii) Current Ratio 3 : 2; (iii) Acid Test Ratio 1.125 :1; (iv) Stock Turnover Ratio 4 times; (v) Fixed Assets
Answer:

Question 22.
From the following information calculate Gross Profit Ratio, Stock Turnover Ratio and Debtors Turnover Ratio.

(Ans : Gross Profit Ratio 20%; Stock Turnover Ratio 4 times; Debtors Turnover Ratio 9.4 times)
Answer:

These NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts. https://mcq-questions.com/ncert-solutions-for-class-12-maths-chapter-7-ex-7-1/

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.1

Question 1.
sin 2x
Solution:

Question 2.
cos 3x
Solution:

Question 3.
\({ e }^{ 2x }\)
Solution:

Question 4.
(ax + c)²
Solution:

Question 5.
sin 2x – 4 e^3x
Solution:

∴ An anti derivative of sin2x – 4e^3x is – \(\frac { 1 }{ 2 }\) cos 2x – \(\frac { 4 }{ 3 }\)4e^3x

Question 6.
\(\int { \left( { 4e }^{ 3x }+1 \right) dx } \)
Solution:

Question 7.
\(\int { { x }^{ 2 }\left( 1-\frac { 1 }{ { x }^{ 2 } } \right) dx } \)
Solution:
\(=\int { { x }^{ 2 }\left( 1-\frac { 1 }{ { x }^{ 2 } } \right) }dx
= ∫(x² – 1)dx
= ∫x² dx – ∫1 dx
= [latex]\frac { { x }^{ 3 } }{ 3 }\) – x + C

Question 8.
\(\int { { (ax }^{ 2 }+bx+c)dx } \)
Solution:
\(\int { { (ax }^{ 2 }+bx+c)dx } \)
= a∫x² dx + b ∫x dx + c∫1 dx
= \(\frac { { ax }^{ 3 } }{ 3 } +\frac { { bx }^{ 2 } }{ 2 }\) + cx + C

Question 9.
\(\int { \left( { 2x }^{ 2 }+{ e }^{ x } \right) dx } \)
Solution:
\(\int { \left( { 2x }^{ 2 }+{ e }^{ x } \right) dx } \)
= 2∫x² dx + ∫e^x dx
= 2 \(\frac { { x }^{ 3 } }{ 3 }\) + e^x + C
= \(\frac { { 2x }^{ 3 } }{ 3 } +{ e }^{ x }\) + C

Question 10.
\(\int { { \left[ \sqrt { x } -\frac { 1 }{ \sqrt { x } } \right] }^{ 2 }dx } \)
Solution:

Question 11.
\(\int { \frac { { x }^{ 3 }+{ 5x }^{ 2 }-4 }{ { x }^{ 2 } } dx } \)
Solution:

Question 12.
\(\int { \frac { { x }^{ 3 }+3x+4 }{ \sqrt { x } } dx } \)
Solution:

Question 13.
\(\int { \frac { { x }^{ 3 }-{ x }^{ 2 }+x-1 }{ x-1 } dx } \)
Solution:
\(=\int { \frac { { x }^{ 2 }(x-1)+(x-1) }{ x-1 } dx } \)
\(=\int { \left( { x }^{ 2 }+1 \right) dx } =\frac { { x }^{ 3 } }{ 3 } +x+c \)

Question 14.
\(\int { \left( 1-x \right) \sqrt { x } dx } \)
Solution:

Question 15.
\(\int { \sqrt { x } \left( { 3x }^{ 2 }+2x+3 \right) dx } \)
Solution:

Question 16.
\(\int { (2x – 3cosx+{ e }^{ x })dx } \)
Solution:
\(\int { (2x – 3cosx+{ e }^{ x })dx } \)
= 2∫x dx – 3∫cosx dx + ∫e^x dx
= 2(\(\frac { { x }^{ 2 } }{ 3 }\)) – 3 sin x + e^x + C
\(={ x }^{ 2 }-3sinx+{ e }^{ x }\) + C

Question 17.
\(\int { \left( { 2x }^{ 2 }-3sinx+5\sqrt { x } \right) dx } \)
Solution:

Question 18.
\(\int { secx(secx+tanx)dx } \)
Solution:
\(\int { secx(secx+tanx)dx } \)
= \(\int\left(\sec ^{2} x+\sec x \tan x\right) d x\)
= ∫sec² x dx + ∫sec x tan x dx
= tan x + sec + C

Question 19.
\(\int { \frac { { sec }^{ 2 }x }{ { cosec }^{ 2 }x } dx } \)
Solution:
= \(\int { \frac { 1 }{ { cos }^{ 2 }x } } { sin }^{ 2 }xdx\)
= \(\int { tan } ^{ 2 }xdx\quad\)
= \(\int\left(\sec ^{2} x-1\right) d x\)
= tanx – x + c

Question 20.
\(\int { \frac { 2-3sinx }{ { cos }^{ 2 }x } dx } \)
Solution:
= \(\int { \left( \frac { 2 }{ { cos }^{ 2 }x } -3\frac { sinx }{ { cos }^{ 2 }x } \right) dx } \)
= \(\int { ({ 2sec }^{ 2 }x-3secxtanx)dx }\)
= 2tanx – 3secx + c

Choose the correct answer in Exercises 21 and 22.

Question 21.
The anti derivative \(\left( \sqrt { x } +\frac { 1 }{ \sqrt { x } } \right) \) equals
(a) \(\frac { 1 }{ 3 } { x }^{ \frac { 1 }{ 3 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c\)
(b) \(\frac { 2 }{ 3 } { x }^{ \frac { 2 }{ 3 } }+{ \frac { 1 }{ 2 } x }^{ 2 }+c\)
(c) \(\frac { 2 }{ 3 } { x }^{ \frac { 3 }{ 2 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c\)
(d) \(\frac { 3 }{ 2 } { x }^{ \frac { 3 }{ 2 } }+\frac { 1 }{ 2 } { x }^{ \frac { 1 }{ 2 } }+c\)
Solution:
(c) \(\frac { 2 }{ 3 } { x }^{ \frac { 3 }{ 2 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c\)

Question 22.
If \(\frac { d }{ dx } f(x) = { 4x }^{ 3 } -\frac { 3 }{ { x }^{ 4 } } \) such that f(2) = 0 then f(x) is
(a) \({ x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } -\frac { 129 }{ 8 } \)
(b) \({ x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } +\frac { 129 }{ 8 } \)
(c) \({ x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } +\frac { 129 }{ 8 } \)
(d) \({ x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } -\frac { 129 }{ 8 } \)
Solution:
(a) \({ x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } -\frac { 129 }{ 8 } \)

These NCERT Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise Questions and Answers are prepared by our highly skilled subject experts. https://mcq-questions.com/ncert-solutions-for-class-12-maths-chapter-4-miscellaneous-exercise/

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise

Question 1.
Prove that the determinant \(\left|\begin{array}{ccc}
x & \sin \theta & \cos \theta \\
-\sin \theta & -x & 1 \\
\cos \theta & 1 & x
\end{array}\right|\) is independent of θ.
Solution:

Question 2.
Without expanding the determinant, prove that \(\left|\begin{array}{lll}
a & a^{2} & b c \\
b & b^{2} & c a \\
c & c^{2} & a b
\end{array}\right|=\left|\begin{array}{lll}
1 & a^{2} & a^{3} \\
1 & b^{2} & b^{3} \\
1 & c^{2} & c^{3}
\end{array}\right|\)
Solution:

Question 3.
Evaluate \(\left|\begin{array}{ccc}
\cos \alpha \cos \beta & \cos \alpha \sin \beta & -\sin \alpha \\
-\sin \beta & \cos \beta & 0 \\
\sin \alpha \cos \beta & \sin \alpha \sin \beta & \cos \alpha
\end{array}\right|\)
Solution:

Question 4.
If a, b and c are real numbers, and ∆ = \(\left|\begin{array}{lll}
b+c & c+a & a+b \\
c+a & a+b & b+c \\
a+b & b+c & c+a
\end{array}\right|\) = 0 Show that either a + b + c = 0 or a = b = c.
Solution:

Expanding along C,
= 2(a + b + c) ((c – b)(b – c) – (a- b)(a – c))
= 2(a + b + c) (bc – c² – b² + bc – a² + ac + ab – bc)
= – (a + b + c) (2a² + 2b² + 2c² – 2ab – 2bc – 2ac)
= – (a + b + c) (a² + b² – 2ab + b² + c² – 2bc + c² + a² – 2ac)
= – (a + b + c) ((a – b)² + (b – c)² + (c – a)²)
∴ \(\left|\begin{array}{lll}
b+c & c+a & a+b \\
c+a & a+b & b+c \\
a+b & b+c & c+a
\end{array}\right|\) ⇒ – (a + b + c)((a – b)² + (b – c)² + (c – a)²) = 0
⇒ (a + b + c) = 0 or (a – b)² + (b – c)² + (c – a)² = 0
⇒ a + b + c = 0 or a – b = 0, b – c = 0 and c – a = 0
⇒ a + b + c = 0 or a = b = c

Question 5.
Solve the equation \(\left|\begin{array}{ccc}
x+a & x & x \\
x & x+a & x \\
x & x & x+a
\end{array}\right|\) = 0, a ≠ 0
Solution:

Question 6.
Prove that \(\left|\begin{array}{ccc}
a^{2} & b c & a c+c^{2} \\
a^{2}+a b & b^{2} & a c \\
a b & b^{2}+b c & c^{2}
\end{array}\right|\) = 4a²b²c²
Solution:

Question 7.
If A^-1 = \(=\left[\begin{array}{ccc}
3 & -1 & 1 \\
-15 & 6 & -5 \\
5 & -2 & 2
\end{array}\right]\) and B = \(\left[\begin{array}{ccc}
1 & 2 & -2 \\
-1 & 3 & 0 \\
0 & -2 & 1
\end{array}\right]\), find (AB)^-1
Solution:

Question 8.
Let A = \(\left[\begin{array}{ccc}
1 & -2 & 1 \\
-2 & 3 & 1 \\
1 & 1 & 5
\end{array}\right]\). Verify that i. [adj A]^-1 = adj(A^-1) ii. (A^-1)^-1 = A
Solution:

From (1) and (2) we get (adj A)^-1 = adj(A^-1).

Question 9.
Evaluate \(\left|\begin{array}{ccc}
x & y & x+y \\
y & x+y & x \\
x+y & x & y
\end{array}\right|\)
Solution:

Question 10.
Evaluate \(\left|\begin{array}{ccc}
1 & x & y \\
1 & x+y & y \\
1 & x & x+y
\end{array}\right|\)
Solution:

Question 11.
\(\left|\begin{array}{lll}
\alpha & \alpha^{2} & \beta+\gamma \\
\beta & \beta^{2} & \gamma+\alpha \\
\gamma & \gamma^{2} & \alpha+\beta
\end{array}\right|\) = (α – ß) (ß – γ) (γ – α) (α + ß + γ)
Solution:

Taking out (ß – α) from R₂ and (γ – α) from
R₃
Expanding along C₃,
= (α + ß + γ)(γ – α)(γ – α)(γ + α – ß – α)
= (α + ß + γ )(ß – α)(γ – α)(γ – ß)
= (ß – γ)(γ – α)(α – ß)(α + ß + γ)

Question 12.
\(\left|\begin{array}{lll}
x & x^{2} & 1+p x^{3} \\
y & y^{2} & 1+p y^{3} \\
z_{1} & z^{2} & 1+p z^{3}
\end{array}\right|\) = (1 + pxyz) (x – y) (y – z) (z – x)
Solution:

Expanding along C₁,
= (1 + pxyz) (y – x) (z – x) (z + x – y – x)
= (1 + pxyz) (y – x) (z – x) (z – y)
= (1 + pxyz) (x – y) (y – z) (z – x)

Question 13.
\(\left|\begin{array}{ccc}
3 a & -a+b & -a+c \\
-b+a & 3 b & -b+c \\
-c+a & -c+b & 3 c
\end{array}\right|\) = 3(a + b + c) (ab + bc + ca)
Solution:

Expanding along C₁,
(a + b + c)\(\left|\begin{array}{ll}
2 b+a & -b+a \\
-c+a & 2 c+a
\end{array}\right|\)
= (a + b + c) [(2b + a) (2c + a) – (a – c) (a – b)]
= (a + b + c) [4bc + 2ab + 2ca + a² – (a² – ab – ac + bc)]
= (a + b + c) [3bc + 3ab + 3ac] = 3 (a + b + c) (ab + bc + ca)

Question 14.
\(\left|\begin{array}{ccc}
1 & 1+p & 1+p+q \\
2 & 3+2 p & 4+3 p+2 q \\
3 & 6+3 p & 10+6 p+3 q
\end{array}\right|\) = 1.
Solution:

Question 15.
\(\left|\begin{array}{lll}
\sin \alpha & \cos \alpha & \cos (\alpha+\delta) \\
\sin \beta & \cos \beta & \cos (\beta+\delta) \\
\sin \gamma & \cos \gamma & \cos (\gamma+\delta)
\end{array}\right|\) = 0
Solution:

Question 16.
Solve the system of the following equations \(\frac { 2 }{ x }\) + \(\frac { 3 }{ y }\) + \(\frac { 10 }{ z }\) = 4
\(\frac { 4 }{ x }\) – \(\frac { 6 }{ y }\) + \(\frac { 5 }{ z }\) = 1
\(\frac { 6 }{ x }\) + \(\frac { 9 }{ y }\) – \(\frac { 20 }{ z }\) = 2
Solution:
Let \(\frac { 1 }{ x }\) = a, \(\frac { 1 }{ y }\) = b and \(\frac { 1 }{ z }\) = c
∴ The given equations become
2a + 3b + 10c = 4
4a – 6b + 5c = 1
6a + 9b – 20c = 2
The equations can be written in the form AX = B
Where A = \(\left[\begin{array}{ccc}
2 & 3 & 10 \\
4 & -6 & 5 \\
6 & 9 & -20
\end{array}\right]/latex]; X = [latex]\left[\begin{array}{l}
a \\
b \\
c
\end{array}\right]\); B = \(\left[\begin{array}{l}
4 \\
1 \\
2
\end{array}\right]\)

∴ a = \(\frac { 1 }{ 2 }\); \(\frac { 1 }{ 3 }\) = b and \(\frac { 1 }{ 15 }\) = c
Hence x = \(\frac { 1 }{ a }\) = 2; y = \(\frac { 1 }{ b }\) = 3; z = \(\frac { 1 }{ c }\) = 5

Question 17.
If a, b, c are in A.P. then determinant
\(\left|\begin{array}{lll}
x+2 & x+3 & x+2 a \\
x+3 & x+4 & x+2 b \\
x+4 & x+5 & x+2 c
\end{array}\right|\) is
a. 0
b. 1
c. x
d. 2x
Solution:
a. 0

Question 18.
If x, y, z are nonzero real numbers, then the inverse of matrix A = \(\left[\begin{array}{lll}
x & 0 & 0 \\
0 & y & 0 \\
0 & 0 & z
\end{array}\right]\) is
a. \(\left[\begin{array}{ccc}
x^{-1} & 0 & 0 \\
0 & y^{-1} & 0 \\
0 & 0 & z^{-1}
\end{array}\right]\)

b. \(x y z\left[\begin{array}{ccc}
x^{-1} & 0 & 0 \\
0 & y^{-1} & 0 \\
0 & 0 & z^{-1}
\end{array}\right]\)

c. \(\frac{1}{x y z}\left[\begin{array}{lll}
x & 0 & 0 \\
0 & y & 0 \\
0 & 0 & z
\end{array}\right]\)

d. \(\frac{1}{x y z}\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]\)
Solution:

Question 19.
Let A = \(\left[\begin{array}{ccc}
1 & \sin \theta & 1 \\
-\sin \theta & 1 & \sin \theta \\
-1 & -\sin \theta & 1
\end{array}\right]\), where 0 ≤ θ ≤ 2π. Then
a. Det (A) = 0
b. Det (A) ∈ (2, ∞)
c. Det (A) ∈ (2, 4)
d. Det (A) ∈ [2, 4]
Solution:
d. Det (A) ∈ [2, 4]