# Class 8 - Math Test - 2

1. If P and Q are two sets and its cardinal number n(P) = 25, n(Q) = 15, and n(P ∪ Q) = 30 then n(P ∩ Q) is ______?

2. If n(P − Q) = 21, n(Q − P) = 26 and n(P ∩ Q) = 9, find n(Q).

3. If set P = {a, b, c, d, e, f, g), Q = {a, d, e, f, g, h), then find P − Q.

4. If P = {a, b, c, d, e, f, g, h}, Q = {c, d, e, i, k, l, m, n} and R = {a, f, k, l, v, w}, then find P ∪ Q.

5. If universe set U = {10, 20, 30, 40, 50, 60, 70, 80, 90}, P = {10, 20, 30, 40, 50, 60} Q = {40, 60, 80, 90}, then find (P ∩ Q)'.

6. n(U) = 30, n(P') = 15, and n(P ∩ Q)' = 20 and n(Q) = 15, find n(Q − P) =?

7. Marked price of item is Rs. 600 and it sold for Rs. 520. What is the discount and discount %?

8. Find the single discount equivalent to two successive discounts of 35% and 7%.

9. When 10% G.S.T. is added on the purchase of a doormat of Rs. 150 then, find the buying price of doormat.

10. The man bought a refrigerator for Rs. 45350 including a GST of 12%. Find the price of refrigerator before GST was added.

11. A shopkeeper purchased a BP Machine for Rs. 800. He sells it at a discount of 20% and still makes a profit of 10%. Find its selling price and marked price.

12. The marked price of iron is Rs. 3000. A shopkeeper allows two successive discounts of 15% and 10%. Find the price which a customer must pay for the Refrigerator.

13. Shreyashi invested Rs 20000 in a company, she would be paid interest at 6% per annum compounded annually. Find the amount received by him at the end of 2 years and the interest for the 3rd year.

14. Calculate the difference between the compound interest and the simple interest on Rs 25000 in 3 years at 5% per annum.

15. Sobha borrowed from a bank Rs 2000 to purchase a sewing machine. If the rate of interest is 5% per annum, what is the compound interest that she has to pay after 2 years?

16. When simple interest on Rs 3.3 lakhs at 6.5% per annum is Rs 75075. Find the time ?

17. The length and breadth of a rectangular park are in the ratio 3 : 4. If the area of the park is 4800 square metres, find the cost of surrounding the park with a fence at the rate of Rs. 2.50 per metre.

18. The area of a trapezium is 400 m^{2}, the distance between two parallel sides is 20 m and one of the parallel side is 15 m. Find the other parallel side.

19. A cylinder of maximum volume is cut from an iron cuboid of length 21 cm and cross-section a square of side 16 cm. Find the volume of the cylinder and the volume of the iron wasted.

20. The sum of the radius and height of a cylinder is 35 cm and the total surface area of the cylinder is 1760 cm^{2}. Find the height and the volume of the cylinder.

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