
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 and his father be x years and y years respectively.
According to question,
7 years ago, we have
x – 7 = 7 (y  7)
Or, x – 7 = 7y – 49
Or, x – 7y =  42 …………… (1)
3 years from now, we have
(x + 3) = 3 (y + 3)
Or, x + 3 = 3y + 9
Or, x – 3y = 6 ……………. (2)
Graphical Representation
From equation (1), x – 7y = 42
Table value of x and y
x:
0
42
35
y:
6
0
1
From equation (2), x – 3y = 6
Table value of x and y
x:
0
9
6
y:
2
1
0
Plotting the tables on the graph:
Q2 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. Ans: Let the cost of one bat and one ball be x Rupees and y Rupees respectively.
According to first condition,
3x + 6y = â‚¨ 3900 …………….(1)
According to second condition,
x + 3y = â‚¨ 1300 …………….(2)
Graphical Representation
From equation (1), 3x + 6y = 3900
Table value of x and y
x:
100
300
700
y:
600
500
300
From equation (2), x + 3y = 1300
Table value of x and y
x:
100
700
400
y:
400
200
300
1 Unit = 100
Q3 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. Ans: Let the cost of one kg apple be x â‚¨ and 1 kg grapes be y â‚¨.
According to first condition,
2x + y = 160 â‚¨ …………..(1)
According to second condition,
4x + 2y = 300
2x + y = 150 ……………….(2)
Graphical Representation
Table for equation (1), 2x + y = 160
Table value of x and y
x:
40
60
80
y:
60
40
0
Table for equation (2), 2x + y = 150
Table value of x and y
x:
40
60
20
y:
70
30
110