Class 8 Maths Chapter 11 Question Answers - Direct and Inverse Proportions

Q1: The volume of a gas V varies inversely as the pressure P for a given mass of the gas. Fill in the blank spaces in the following table:

Ans: Since volume and pressure are inversely proportional.
PV = K


Hence the completed table is


Q2: Six pumps working together empty a tank in 28 minutes. How long will it take to empty the tank if 4 such pumps are working together?
Ans: Let the required time be t minutes.

Less pump → More time
Since there is an inverse variation.
x₁y₁ = x₂y₂
6 × 28 = 4 × x
x = 42
Hence, the required time = 42 minutes.

Q3: A garrison of 120 men has provisions for 30 days. At the end of 5 days, 5 more men joined them. How many days can they sustain on the remaining provision?
Ans: Let the number of days be x.

[∵ Remaining days = 30 – 5 = 25] [Total men = 120 + 5 = 125] Since there is an inverse variation.
x₁y₁ = x₂y₂
120 × 25 = 125 × x
x = 24
Hence, the required number of days be 24.

Q4: If two cardboard boxes occupy 500 cubic centimetres space, then how much space is required to keep 200 such boxes?
Ans: As the number of boxes increases, the space required to keep them also increases.
So, this is a case of direct proportion.

Thus, the required space is 50,000 cubic centimetres.

Q5: The cost of 5 metres of cloth is ₹ 210. Tabulate the cost of 2, 4, 10 and 13 metres of cloth of the same type.
Ans: Let the length of the cloth be x m and its cost be ₹ y. We have the following table.
Since x and y are directly proportional



Q6: Mohit deposited a sum of ₹ 12000 in a Bank at a certain rate of interest for 2 years and earns an interest of ₹ 900. How much interest would be earned for a deposit of ₹ 15000 for the same period and at the same rate of interest?
Ans: Let the required amount of interest be ₹ x.


Q7: In a scout camp, there is food provision for 300 cadets for 42 days. If 50 more persons join the camp, for how many days will the provision last?
Ans: More the persons, the sooner would be the provision exhausted. So, this is a case of inverse proportion.
Let the required number of days be x.
Hence, 300 × 42 = (300 + 50) × x
300 × 42 = 350 × x
x = 36