Chapter 10: Direct and Inverse Proportions

Example 1: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
Solution:The correct answer is (c).
Example 2: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)45km/h2
(c)70 km/h(d)45 km/h
Solution: The correct answer is (a).
Example 3: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.
Solution:The correct answer is (b).
[Because, in a fixed time interval, as the speed of a vehicle increases, the distance travelled by it also increases in the same ratio.]

1.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
2.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
3.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.
4.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.

5.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
6.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
7.In which of the following case, do the quantities vary directly with each other?
(a)x0.52832 y2832128
(b)p12223242 q13233343
(c)r25102550 s2510520.5
(d)u246912 v189643
8.Which quantities in the previous question vary inversely with each other?
(a)x and y(b)p and q(c)r and s(d)u and v
9.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.
10.Both x and y are in direct proportion, then x1and y1 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.

11.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
12.100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for
(a)30 days(b)965days
(c)120 days(d)40 days
13.If two quantities x and y vary directly with each other, then
(a)x/y remains constant.(b)x – y remains constant.
(c)x + y remains constant.(d)x × y remains constant.
14.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)p – q remains constant.
15.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)250/9m(b)500/9m(c)1000 m(d)500/3m

16.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
Fill in the blanks to make the statements true:
17.If x = 5y, then x and y vary ______ with each other.
18.If xy = 10, then x and y vary ______ with each other.
19.When two quantities x and y are in ______ proportion or vary ______ they are written as x ∝ y.
20.When two quantities x and y are in _______ proportion or vary ______ they are written as x ∝y
21.Both x and y are said to vary ______ with each other if for some positive number k, xy = k.
22.x and y are said to vary directly with each other if for some positive number k, ______ =k.
23.Two quantities are said to vary ______ with each other if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.
24.Two quantities are said to vary ______ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant.
25.If 12 pumps can empty a reservoir in 20 hours, then time required by 45 such pumps to empty the same reservoir is ______ hours.

26.If x varies inversely as y, then x – 60 y 2 10
27.If x varies directly as y, then x 12 6 y 48 –
28.When the speed remains constant, the distance travelled is ______ proportional to the time.
29.On increasing a, b increases in such a manner that b a remains______
and positive, then a and b are said to vary directly with each other.
30.If on increasing a, b decreases in such a manner that _______ remains ______ and positive, then a and b are said to vary inversely with each other.
31.If two quantities x and y vary directly with each other, then ______ of their corresponding values remains constant.
32.If two quantities p and q vary inversely with each other then ______ of their corresponding values remains constant.
33.The perimeter of a circle and its diameter vary _______ with each other.
34.A car is travelling 48 km in one hour. The distance travelled by the car in 12 minutes is _________.
35.An auto rickshaw takes 3 hours to cover a distance of 36 km. If its speed is increased by 4 km/h, the time taken by it to cover the same distance is __________.
36.If the thickness of a pile of 12 cardboard sheets is 45 mm, then the thickness of a pile of 240 sheets is _______ cm.
37.If x varies inversely as y and x = 4 when y = 6, then when x = 3 the value of y is _______.
38.In direct proportion, 11ab _______ 22ab

39.In case of inverse proportion, 2a−=2b−
40.If the area occupied by 15 postal stamps is 60 cm2, then the area occupied by 120 such postal stamps will be _______.
41.If 45 persons can complete a work in 20 days, then the time taken by 75 persons will be ______ hours.
42.Devangi travels 50 m distance in 75 steps, then the distance travelled in 375 steps is _______ km.