 # Direct and Inverse Proportions

40. Two quantities are said to vary directly with each other if

(A) they increase (or decrease) together in such a manner that the ratio of their corresponding values remains constant

(B) an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant

(C) Both of these

(D) None of these

39. Two quantities are said to vary inversely with each other if

(A) they increase (or decrease) together in such a manner that the ratio of their

corresponding values remains constant

(B) an increase in one causes a decrease in the other in such a manner that the

product of their corresponding values remains constant

(C) Both of these

(D) None of these

38. When two quantities x and y are in direct proportion (or vary directly), it can be written as

(A) x ­∝ y

(B) x ­∝ 1/y

(C) y ­∝ 1/x

(D) xy ­∝ 1

37. When two quantities x and y are in inverse proportion (or vary inversely), it can be written as

(A) x ­∝ y

(B) x ­∝ 1/y

(C) xy ­∝ 1

(D) None of these

36. If x and y are inversely proportional then which of the following is true?

(A) x = ky

(B) xy = k

(C) y = ky

(D) x + y = k

35. Both x and y are in direct proportion, then 1/x and 1/y are

(A) in indirect proportion.

(B) in inverse proportion.

(C) neither in direct nor in inverse proportion.

(D) sometimes in direct and sometimes in inverse proportion.

34. Which of the following vary inversely with each other?

(A) speed and distance covered.

(B) distance covered and taxi fare.

(C) distance travelled and time taken.

(D) speed and time taken.

33. Which of the following is in direct proportion?

(A) One side of a cuboid and its volume.

(B) Speed of a vehicle and the distance travelled in a fixed time interval.

(C) Change in weight and height among individuals.

(D) Number of pipes to fill a tank and the time required to fill the same tank.

32. What type of proportion is there between a rhombus and its perimeter?

(A) Direct

(B) Inverse

(C) Both of these

(D) None of these

31. Assuming land to be uniformly fertile, the area of land and the yield on it vary

(A) directly with each other.

(B) inversely with each other.

(C) neither directly nor inversely with each other.

(D) sometimes directly and sometimes inversely with each other.

30. The number of teeth and the age of a person vary

(A) directly with each other.

(B) inversely with each other.

(C) neither directly nor inversely with each other.

(D) sometimes directly and sometimes inversely with each other.

29. If one angle of a triangle is kept fixed,  then the measure of the remaining two angles are related

(A) directly

(B) inversely

(C) Both of these

(D) None of these

28. For fixed time period and rate of interest, the simple interest and the principal is related

(A) directly

(B) inversely

(C) Both of these

(D) None of these

27. The area of cultivated land and the crop harvested is a case of

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

26. Income tax and the income is a case of

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

25. The distance travelled by CNG bus and the amount of CNG used is a case of

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

24. Area of the walls of a room and the cost of white washing the walls is a case of

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

23. Compound interest on a given sum and the sum invested is a case of

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

22. Increase in cost and number of shirts that can be purchased if the budget remains the same is a case of

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

21. If two quantities x and y vary directly with each other, then

(A) x/y remains constant

(B) xy remains constant.

(C) x + y remains constant

(D) x × y remains constant.

20. If two quantities p and q vary inversely with each other, then

(A) p/q remains constant

(B) p + q remains constant

(C) p × q remains constant

(D) pq remains constant

19. If x = 5y, then x and y varies

(A) directly with each other

(B) inversely with each other

(C) neither directly nor inversely with each other

(D) sometimes directly and sometimes inversely with each other

18. If xy = 10, then x and y varies

(A) directly with each other

(B) inversely with each other

(C) neither directly nor inversely with each other

(D) sometimes directly and sometimes inversely with each other

17. If x and y are directly proportional and when x = 13, y = 39, which of the following is not a possible pair of corresponding values of x and y?

(A) 1 and 3

(B) 17 and 51

(C) 30 and 10

(D) 6 and 18

16. A car covers a distance in 40 minutes with an average speed of 60 km per hour. The average speed to cover the same distance in 30 minutes is

(A) 80 km/h

(B) 45/2 km/h

(C) 70 km/h

(D) 45 km/h

15. Amrita takes 18 hours to travel 720 kilometres. Time taken by her to travel 360 kilometres is

(A) 8 hours

(B) 4.5 hours

(C) 7 hours

(D) 9 hours

14. If the cost of 10 pencils is ₹90, then the cost of 19 pencils is

(A) ₹170

(B) ₹171

(C) ₹172

(D) ₹175

13. If 5 persons can finish a job in 10 days, then one person will finish it in

(A) 2 days

(B) 10 days

(C) 50 days

(D) None of these

12. Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?

(A) 2 and 3

(B) 8 and 12

(C) 15 and 20

(D) 25 and 37.5

11. Both x and y vary inversely with each other. When x is 10, y is 6, which of the following is not a possible pair of corresponding values of x and y?

(A) 12 and 5

(B) 15 and 4

(C) 25 and 2.4

(D) 45 and 1.3

10. A truck needs 54 litres of diesel for covering a distance of 297 km. The diesel required by the truck to cover a distance of 550 km is

(A) 100 litres

(B) 50 litres

(C) 25.16 litres

(D) 25 litres

9. By travelling at a speed of 48 kilometres per hour, a car can finish a certain journey in 10 hours. To cover the same distance in 8 hours, the speed of the car should be

(A) 60 km/h

(B) 80 km/h

(C) 30 km/h

(D) 40 km/h

8. Meenakshee cycles to her school at an average speed of 12 km/h and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be

(A) 20/3 km/h

(B) 16 km/h

(C) 20 km/h

(D) 15 km/h

7. 100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for

(A) 30 days

(B) 96/5 days

(C) 120 days

(D) 40 days

6. If the distance travelled by a rickshaw in one hour is 10 km, then the distance travelled by the same rickshaw with the same speed in one minute is

(A) 250/9 m

(B) 500/9 m

(C) 1000 m

(D) 500/3 m

5. Both x and y vary directly with each other and when x is 10, y is 14, which of the following is not a possible pair of corresponding values of x and y?

(A) 25 and 35

(B) 35 and 25

(C) 35 and 49

(D) 15 and 21

4. If 12 pumps can empty a reservoir in 20 hours, then time required by 45 such pumps to empty the same reservoir is

(A) 65 hours

(B) 75 hours

(C) 80 hours

(D) 85 hours

3. If x and y are in direct proportion, then (x – 1) and (y – 1) are in

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

2. If x and y are in inverse proportion, then (x + 1) and (y + 1) are also in

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these

1. If p and q are in inverse variation then (p + 2) and (q – 2) are in

(A) direct proportion

(B) inverse proportion

(C) Both of these

(D) None of these