In this Page, you will learn how to solve questions of Ex 3.1 Class 10 Maths NCERT Solutions recommended in CBSE 10th Board Maths Exam syllabus.
These NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1
Question 1.
Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting)? Represent this situation algebraically and graphically.
Solution:
Let Aftab’s present age be x and his daughter’s present age by y.
∴ Seven years ago,
Aftab’s age was x – 7
and his daughter’s age was y – 7
According to question
(x – 7) = 7 (y – 7)
or, x – 7 = 7y – 49
or, x – 7y + 42 = 0 … (i)
In case II
Three vears hence
Aftab’s age will be = x + 3
and his daughter’s age will be = y + 3
Again, according to question,
(x + 3) = 3(y + 3)
or, x + 3 = 3y + 9
or, x – 3y – 6 = 0 … (ii)
From equation (i)
x – 7y + 42 = 0
x = 7y – 42
Now from equation (ii)
x – 3y – 6 = 0
x = 3y + 6
x – 7y + 42=0
x – 3y – 6 = 0
Subtracting both equations
4y = 48
y = 12
Putting this value in equation (ii)
x – 3(12) – 6 = 0
x – 36 – 6 = 0
x = 2
Hence the age of Aftab is 42 years and his daughter is 12 years old.
Question 2.
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.
Solution:
Let the cost of each bat = x
and the cost of each ball = y
Then the algebric representation is given by the following equation.
Question 3.
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300. Represent the situation algebraically and geometrically.
Solution:
Let cost of one kg of apples = ₹ x
and the cost of one kg of grapes = ₹ y
Then the algebric representation is given by the following equations :
