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

NCERT Solutions for Maths Chapter 3, Exercise 3.1 involve complete answers for each question in the exercise 3.1. The solutions provide students a strategic methods to prepare for their exam. Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1 questions and answers helps students to perform better in exam and it will clear doubts definitely. Students will find it extremely easy to understand the questions and learn solving the problems. NCERT Solutions for Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1 prepared by www.mathematicsandinformationtechnology.com team in very delicate, easy and creative way.

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 1:

Let the present age of Aftab be x.

And, present age of his daughter = y

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 = 7 y - 49

x - 7 y = -42 ---------------------------(1)

Three years hence,

Age of Aftab = x + 3

Age of his daughter = y + 3

According to the question,

(x+3) = 3 ( y + 3 )

x + 3= 3 y + 9

x - 3 y = 6 -----------------------------(2)

Therefore, the algebraic representation is

For x – 7 y = − 42,

x = − 42 + 7 y

The solution table is

x	-7	0	7
y	5	6	7

For x – 3y = 6

x = 6 + 3y

The solution table is

x	6	3	0
y	0	-1	-2

The graphical representation is as follows.

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.

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 2:

Let the cost of a bat be Rs x.

And, cost of a ball = Rs y

According to the question, the algebraic representation is

3 x + 6 y = 3900

x + 2 y = 1300

For 3 x + 6 y = 3900

x = 3900 -6 y / 3

The solution table is

x	300	100	-100
y	500	600	700

For x + 2 y = 1300

x = 1300 – 2 y ,

The solution table is

x	300	100	-100
y	500	600	700

The graphical representation is as follows:

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.

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 3: Let the cost of 1 kg of apples be Rs x.

And, cost of 1 kg of grapes = Rs y

According to the question, the algebraic representation is

2 x + y = 160

4x + 2y = 300

For y = 160 – 2x

The solution table is

x	50	60	70
y	60	40	20

For 4x + 2y = 300,

y=300 - 4 x / 2

The solution table is

x	70	80	75
y	10	-10	0

The graphical representation is as follows:

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.