# Pair of Linear Equations in Two Variables - Class 10 Math CBSE Guide NCERT Solutions of Exercise 3.1

## Class 10 Mathematics - CBSE Guide NCERT Solutions

### Chapter 3 Pair of Linear Equations in Two Variables

#### NCERT Solutions of Math Textbook 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 the present age of Aftab and his daughter are be x and y respectively.
Seven years ago,
Age of Aftab = x − 7
Age of his daughter = y − 7
According to the question,
( x – 7 ) = 7 (y – 7)
x – 7 = 7y – 49
x – 7y = – 42 ………………… (1)
Three years hence,
Age of Aftab = x + 3 and,
Age of his daughter = y + 3
By the given condition,
(x + 3) = 3(y + 3),
x – 3y = 6 … … … … … .. (2)
Therefore, the algebraic representation is -
x – 7y = – 42
x – 3y = 6
For  x – 7y = – 42,
x = – 42 + 7y
The solution table is -
x = 6 + 3y
The solution table is -

Question 2: The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
Solution:
Let the cost of a bat be Rs x.
And, cost of a ball = Rs y
According to the question, the algebraic representation is -
3x + 6y = 3900
x + 2y = 1300
For 3x + 6y = 3900,

Question 3: The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Solution:
(Student may try to solve taking hint from above problems).
The graphical representation will be as follows -