These NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions InText Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions InText Questions

NCERT Intext Question Page No. 204

Question 1.

Observe the following tables and find if x and y are directly proportional.

Answer:

i. e. each ratio is the same

.’. x and y are directly proportional

i. e. all the ratios are not the same x

and y are not directly proportional.

i.e. all the ratios are not the same

x and y are not directly proportional.

Question 2.

Principal = ₹ 1000, Rate = 8% per annum. Fill in the following table and find which type of interest (simple or compound) change is in direct proportion with time period.

Answer:

Case of Simple Interest

[P = ₹ 1000, r = 8% p.a.]

In each case the ratio is the same.

The simple interest changes in direct proportion with time period.

Case of Compound Interest [P = ₹ 1000, r = 8% p.a.]

\(\frac{\mathrm{CI}}{\mathrm{T}}\) is not the same in each case.

∴ The compound interest does not change in direct proportion with time period.

NCERT Intext Question Page No. 211

Question 1.

Observe the following tables and find which pair of variables (here x and y) are in the inverse proportion.

Answer:

(i) x_{1}y_{1} = 50 x 5 = 250

x_{2}y_{2} = 40 x 6 = 240

x_{1}y_{1} ≠ x_{2}y_{2}

Hence, x and y are not in inverse proportion.

(ii) x_{1}y_{1} = 100 x 60 = 6000

x_{2}y_{2} = 200 x 30 = 6000

x_{3}y_{3} = 300 x 20 = 6000

x_{4}y_{4} = 400 x 15 = 6000

x_{1}y_{1} = x_{2}y_{2} = x_{3}y_{3} = x_{4}y_{4}

Hence x and y are in inverse proportion.

(iii) x_{1}y_{1} = 90 x 10 = 900

x_{2}y_{2} = 60 x 15 = 900

x_{3}y_{3} = 45 x 20 = 900

x_{4}y_{4} = 30 x 25 = 750

x_{1}y_{1} = x_{2}y_{2} = x_{3}y_{3} ≠ x_{4}y_{4}

.’. x and y are not in inverse proportion.

Note: (1) When two quantities x and y are in direct proportion (or vary directly), they are also written is x ∝ y.

(2) When two quantities x and y are in inverse proportion (or very inversely), they are also written as x ∝ \(\frac{1}{y}\).