CBSE Class 8 - Mathematics - Direct and Inverse Proportions

Direct and Inverse Proportions

CBSE Class 8 - Mathematics

NCERT Exemplar Problems and Solutions


Q1: 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

Answer: (c) 30 and 10
For direct variation,

x1	=	x2
y1		y2

Thus x/y = 13/39 = 1/3. Options (a), (b) and (d) have the same ratio while option (c) does not.


Q2: 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.

Answer: (b) Speed of a vehicle and the distance travelled in a fixed time interval.
∵ Speed / distance = fixed ratio.


Q3: 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


Answer: (c) 15 and 20
u/v = 2/3
Option (C) does not maintain the same ratio.




Q4: 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.

Answer: (d) sometimes directly and sometimes inversely with each other.


Q5: 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

Answer:  (a) 100 litres
More diesel means more distance covered. It is a case of direct variation.
∴ 54/297 = x/550
⇒ x = 54 × 550 / 297 = 100


Q6: 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


Answer: (a) 60 km/h
Higher the speed, less time will it take to finish the journey. It is a case of inverse propotion.
∴ 48 × 10 = s × 8
⇒ s = 60


Q7: 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.

Answer: (d) speed and time taken.


Q8: 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.

Answer: (b) in inverse proportion.



Q9: 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

Answer: (a) 30 days
Less people, food will last more days. ⇒ It is an inverse proportion.
∴ 100 × 24 = 80 × days
⇒ days = 30


Q10: (Fill in the blanks)

(a) Amrita takes 18 hours to travel 720 kilometres. Time taken by her to travel 360 kilometres is _______.

(b) If x and y are inversely proportional then _____ = k where k is positive constant.

(c) If x = 5y, then x and y vary ______ with each other.

(d) If xy = 10, then x and y vary ______ with each other.

(e) x and y are said to vary directly with each other if for some positive number k, ______ =k.

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


Answers:
(a) 9 hours [Direct proportion]
(b) xy
(c) directly (∵ x/y = 5 a fixed ratio)
(d) inversely
(e) x/y
(f) 16/3 hours. More pumps means less hours to empty the reservoir.
∴  12 × 20 = 45 x h
⇒ h = 16/3