Page 298 - ICSE Math 7

11. In a class of 40 students, 25 students play football and 20 students play badminton. If each
student play at least one game, find the number of students who play:
(a) only football. (b) only badminton.

12. Let A = {x | 12 < x < 20, x ∈ N}, B = {Set of even numbers between 8 and 18} and
C = {7, 9, 11, 14, 18, 20}, find the following.

(a) (A ∩ B) ∩ C (b) (A ∩ B) ∪ (B ∩ C) (c) (A ∩ C) ∪ B
13. Rahul’s age is mean proportional between the ages of his brother and sister. If Rahul’s age is
4 years and his sister’s age is 8 years, find his brother’s age.
14. A tank has two pipes P and Q. Pipe P fills the tank and pipe Q empties the tank. If only pipe
P is open, then the empty tank is filled in 12 hours and if both the pipes are open, then the
tank is filled in 18 hours. In how much time can the full tank be emptied if only pipe Q is
open?
3 3
15. A sum of ` 25,000 increases by 7% and the resulting amount then decreases by 3 % . Find
the final amount. 5 4
16. In a group of 75 people, 68% like coffee and the rest of them like tea. Find the number of people
who like tea.
17. A shopkeeper bought a washing machine for ` 35,500 and sold it at a loss of 12%. Find the
selling price of the washing machine.

18. A shopkeeper sold two laptops for ` 36,000 each. On one laptop he gained 20% and on the other
he lost 28%. Find his profit or loss per cent.
19. A sum of ` 600 amounts to ` 720 in 4 years at some rate of interest per annum. In how much
time, will ` 800 amounts to ` 1,020 with the same rate of interest?
20. Two friends invested ` 9,000 and ` 12,000 at the same rate of interest per annum. If at the end
of 7 years, one of them receives ` 525 more than the other, find the rate of interest.
2
21. The area of a playground is 8,100 m . If the playground is square in shape, find the time required
–1
by a man to cover its perimeter walking at a speed of 5 m s .
–1
22. A car going at a speed of 82 km h takes 4 h to reach place A from place B. How much time
–1
will it take if its speed is 40 km h ?
2
2
2
2
23. What should be subtracted from 9x y + 5xy – 7y + 3 to get 3y + 7x y – 2xy + 1?
24. The length and breadth of a rectangle is (4a + 2b) cm and (3a – 7b) cm respectively. Find the
perimeter of the rectangle.
25. The length of a rectangle is 5 cm more than its breadth. If its length is increased by 7.8 cm and
breadth is decreased by 3 cm, the area remains unchanged. Find the length and breadth of the
original rectangle.

26. Solve: 4(3x + 2) – 5(x – 2) = 3(4x – 3) + 2
27. Solve the given equation and represent the solution graphically.
8(y – 3) ≤ 6y – 15, y ∈ N

− 3x 4x
28. Solve: + 7 ≤ − 6; x ∈ Z
2 3
29. The sum of two adjacent angles is 105°. If one of them measures 25° less than the other, find
the angles.

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