Class 8 Maths: Inverse Proportions — Practice Questions with Answers

Explanation: More workers finish the same wall in fewer days, so workers and days are in inverse proportion and their product stays constant. 6 × 12 = 72, so days for 8 workers = 72 ÷ 8 = 9 days. The answer 16 days comes from wrongly applying direct proportion, which would make more workers slower.

Explanation: In inverse proportion, when one quantity increases the other decreases so that their product stays constant. For a fixed distance, speed × time = distance, so doubling the speed halves the time taken. In each of the other options, both quantities increase together, which is direct proportion.

Explanation: In inverse proportion, the product x × y stays constant. Here the constant is 4 × 15 = 60, so when x = 6, y = 60 ÷ 6 = 10. Choosing 22.5 treats the relation as direct proportion, and 17 wrongly adds 2 to y just because x increased by 2.

Explanation: Inverse proportion means y = k ÷ x for some fixed number k, which can be rewritten as x × y = k. So the product of the two quantities never changes. A constant ratio x ÷ y describes direct proportion, while the sum and the difference keep changing in both types of proportion.

Explanation: The distance is fixed: 60 × 6 = 360 km. Speed and time are inversely proportional for a fixed distance, so the new speed = 360 ÷ 4 = 90 km/h. The answer 40 km/h uses direct proportion, but a slower speed can never finish the same journey in less time.

Explanation: The total food equals 40 × 30 = 1200 student-days. With 40 + 10 = 50 students, it lasts 1200 ÷ 50 = 24 days. The option 37.5 days uses direct proportion, but more students must finish the food in fewer days, not more.

Explanation: More taps fill the tank faster, so the number of taps and the time taken are in inverse proportion: 8 × 27 = 216. Time for 12 taps = 216 ÷ 12 = 18 minutes. The answer 23 minutes just subtracts 4 minutes because the taps rose by 4, and 40.5 minutes wrongly uses direct proportion.

Explanation: For inverse proportion, every pair must give the same product: p × q = 12 × 10 = 120. Checking the options, 15 × 8 = 120 matches, while 20 × 5 = 100, 14 × 8 = 112 and 24 × 6 = 144 do not. So only p = 15, q = 8 lies on the same relation.

Explanation: Machines and days are in inverse proportion, so machines × days is constant: 9 × 20 = 180 machine-days. With 6 machines, days = 180 ÷ 6 = 30 days. The option 13⅓ days uses direct proportion, but fewer machines must take more time, not less.

Explanation: The total work = pumps × hours per day × days = 6 × 8 × 10 = 480 pump-hours, and this stays fixed. With 8 pumps working for 6 days, hours per day = 480 ÷ (8 × 6) = 480 ÷ 48 = 10 hours. The option 6 hours adjusts only for the extra pumps and forgets that the days have also reduced from 10 to 6.

Explanation: In the first 15 days, 120 soldiers use 120 × 15 = 1800 soldier-days of food out of the total 120 × 45 = 5400, leaving 5400 − 1800 = 3600. Now only 120 − 30 = 90 soldiers remain, so the food lasts 3600 ÷ 90 = 40 more days. The answer 60 days forgets that 15 days of food had already been consumed.

Explanation: Increasing x by 25% makes it 125% = 5/4 of its old value. To keep x × y constant, y must become 4/5 = 80% of its old value, which is a decrease of 100% − 80% = 20%. Assuming y also falls by 25% ignores that inverse proportion works through the product, not through equal percentage changes.