Q1. 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.
Ans: Let the present age of Aftab be ‘x’.
And, the present age of his daughter be ‘y’.
Now, we can write, 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 ………………………(i)
Also, three years from now or after three years,
Age of Aftab will become = x + 3.
Age of his daughter will become = y + 3
According to the situation given,
x + 3 = 3(y + 3)
⇒ x + 3 = 3y + 9
⇒ x − 3y = 6 …………..…………………(ii)
Subtracting equation (i) from equation (ii) we have
(x − 3y) − (x − 7y) = 6 − (−42)
⇒ −3y + 7y = 6 + 42
⇒ 4y = 48
⇒ y = 12
The algebraic equation is represented by
x − 7y = −42
x − 3y = 6
For, x − 7y = −42 or x = −42 + 7y
The solution table is
For, x − 3y = 6 or x = 6 + 3y
The solution table is
The graphical representation is:
Q2. The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically.
Ans: Let us assume that the cost of a bat be ‘Rs x’
And, the cost of a ball be ‘Rs y’
According to the question, the algebraic representation is
3x + 6y = 3900
And x + 3y = 1300
For, 3x + 6y = 3900
Or x = (3900  6y) / 3
The solution table is
For, x + 3y = 1300
Or x = 1300  3y
The solution table is
The graphical representation is as follows:
Q3. The cost of 2 kg of apples and 1kg 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.
Ans: 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;
For 4x + 2y = 300 or y = (300  4x) / 2, the solution table is;
The graphical representation is as follows:
Check out the NCERT Solutions of all the exercises of Linear Equations in Two Variables:
Ex 3.2 NCERT Solutions: Pair of Linear Equations in Two Variables
Ex 3.3 NCERT Solutions: Pair of Linear Equations in Two Variables
Ex 3.4 NCERT Solutions: Pair of Linear Equations in Two Variables
Ex 3.5 NCERT Solutions: Pair of Linear Equations in Two Variables
Ex 3.6 NCERT Solutions: Pair of Linear Equations in Two Variables
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