Page 305 - ICSE Math 8

10. Solve MN + NM = PMP, where MN and NM are 2-digit numbers and PMP is a 3-digit number.
11. Write all the subsets of {–2, 4, 6}.
12. If n(X) = 35, n(Y) = 42 and n(X ∩ Y) = 9, find n(X ∪ Y).

13. Alia’s income is 20% less than that of Priyanka’s. How much per cent is Priyanka’s income more than
that of Alia’s?
14. A number when decreased by 20 % becomes 264. Find the original number.
15. Divide 450 marbles among three friends in the ratio 4 : 5 : 6.

16. Divide ` 6,250 into three parts in such a way that the first part is 62.5% of the second part and the ratio
between the second and third part is 8 : 12.
17. A shop has enough ration to feed 20 families for 6 days. How long would the food last if there were 10
more families?
18. Manoja, Nida and Sandeep can do a piece of work in 8 hours, 15 hours and 12 hours respectively. How
long will it take to finish the work if they work together?
19. Two DVD players are sold at ` 4,500 each. On one there is a profit of 10% and on the other there is a
loss of 10%. What is the profit % or loss % on the whole transaction?
20. Which is a better offer for a customer—a discount of 30% or two successive discounts of 10% and 20%?
21. A builder constructs a house for ` 60,00,000. Due to recession, its value depreciates by 20 % in 4 years.
What value does he get, if he sells this house after 4 years?
22. Find the amount and the compound interest on ` 12,500 at the rate of 6 % per annum for 18 months,
interest being compounded half-yearly.
4
3
3
4
23. What should be subtracted from 16a – 4a + 25a – 40 to get 7a + 12a – 14a – 10?
4
3
2
24. Divide 4x + 10x + 32x + 14x by 4x + 2.
2
25. Evaluate 105 × 102 using (x + a)(x + b) = x + (a + b)x + ab.
26. The length of a square garden is given by (2x + 3) units. Find the area of the garden.
5 2
2 2 4
4 2 2
27. Factorize 36x y z – 54x z + 90x y z
2
2
28. Factorize 4x + 12xy + 9y – 8x – 12y
–1
29. A train is travelling at a speed of 80 km h from Delhi to Kota. On its return journey, it travels at a
–1
speed of 60 km h and takes 2 hours more than the onward journey. What is the distance between Delhi
and Kota?
30. Ranu’s age is two years less than twice his sister Tanu’s age. The sum of twice Ranu’s age and 3 times
Tanu’s age is 66. How old are Ranu and Tanu?
31. Three angles of a quadrilateral are in the ratio 3 : 4 : 5. The sum of the least and the greatest of these is
160º. Find the angles of the quadrilateral.
A D
3x + 1
32. ABCD is a rectangle. Its diagonals meet at point O.
Find x, if OB = 2x + 4 and OA = 3x + 1. 2x + 4 O
B C
33. Construct a quadrilateral PACE in which PA = 5.4 cm, AC = 5.7 cm, PE = 4.5 cm, ∠P = 120º and
∠A = 115º. What is the measure of the side CE?
34. Is it possible to construct a quadrilateral MASK with MA = 5.1 cm, AS = 7.4 cm, ∠M = 80º, ∠A = 140°
and ∠S = 145º? Give reasons for your answer.
35. What is net of a 3D shape? Draw the net of a square pyramid.
36. What are platonic solids? Name any three platonic solids and verify Euler’s formula for them.

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