NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1

Ex 3.1 Class 10 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 present age of Aftab = x years and present age of Aftab’s daughter = y years.

1st Condition :
Seven years ago
x – 7 = 7(y – 7)
⇒ x – 7 = 7y – 49
⇒ x – 7y = – 42
Table :


2nd Condition :
Three years later,
x + 3 = 3(y + 3)
x + 3 = 3y + 9
x – 3y = 6
Table :

Thus, the algebraic equations are
x – 7y + 42 = 0 and x – 3y – 6 = 0

Students can also visit Linear Equations In Two Variables Class 10 Practice Set 1.1 here you can see more solved problems.

Math Class 10 Ex 3.1 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 cost of one bat = ₹ x
and the cost of one ball = ₹y
A.T.Q.
1st Condition :
3x + 6y = 3900
Table :

2nd Condition :
x + 3y = 1300
Table :

Thus, the algebraic equations are 3x + 6y = 3900 and x + 3y – 1300

Class 10 Maths Chapter 3 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

A.T.Q.
1st Condition :
2x + y = 160
Table :

2nd Condition :
4x + 2y = 300
Table :

Thus, algebraic situations are 2x + y = 160 and 4x + 2y = 300

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