NCERT Solutions for Class 10 Maths Chapter 3
Pair of Linear Equations in Two Variables
Exercise 3.1
Page 44
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.
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 = 7y – 49
x – 7y = -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 = 3y + 9
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 |
− 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:-
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.
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+3y = 1300
For 3x + 6y = 3900
x = (3900 – 6y)/3
The solution table is
x |
300 |
100 |
− 100 |
y |
500 |
600 |
700 |
For x+ 3y = 1300
x = 1300 − 3y
The solution table is
x | 1000 | 700 | 400 |
y | 100 | 200 | 300 |
The graphical representation is as follows :-
3. The cost of 2 kg of apples and 1kg 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.
Let the cost of 1 kg of apples be ‘Rs. x’
And, cost of 1 kg of grapes be ‘Rs. y’
According to the question, the algebraic representation is
2x+y = 160
and 4x+2y = 300
For, 2x+y = 160 or y = 160−2x, the solution table is
The solution table is
x |
50 |
60 |
70 |
y |
60 |
40 |
20 |
For 4x + 2y = 300
y = (300-4x)/2
The solution table is
x |
70 |
80 |
75 |
y |
10 |
−10 |
0 |
The graphical representation is as follows :-