Practice Questions
Concept Explanation
Two quantities are in inverse proportion if their product remains constant: x × y = k.
If x₁y₁ = x₂y₂, the quantities vary inversely.
Examples: speed × time = distance (fixed distance); men × days = work (fixed work).
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Q1 EasyIf 6 men can do a piece of work in 12 days, in how many days will 8 men do the same work?ExplanationMen and days are inversely proportional. 6 × 12 = 8 × d → d = 9 days.
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Q2 EasyA car travelling at 60 km/h covers a distance in 5 hours. How long will it take to cover the same distance at 75 km/h?ExplanationSpeed and time are inversely proportional for fixed distance. 60 × 5 = 75 × t → t = 4 hours.
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Q3 EasyX varies inversely as y. If x = 12 when y = 5, what is x when y = 10?Explanationxy = 60. When y = 10, x = 6.
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Q4 EasyIf the speed of a car is doubled, the time taken to cover the same distance becomes:ExplanationSpeed and time are inversely proportional, so time becomes half.
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Q5 EasyIf 4 men can do a work in 18 days, in how many days can 6 men do the same work?Explanation4 × 18 = 6 × d → d = 12 days.
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Q6 EasyIf 5 machines produce a batch in 8 hours, how long will 10 machines take to produce the same batch?Explanation5 × 8 = 10 × t → t = 4 hours.
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Q7 EasyIf x × y = 72 and y increases from 6 to 9, what does x become?Explanationx = 72/9 = 8.
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Q8 MediumIf 15 pumps can raise a certain quantity of water in 8 days, how many days will 10 pumps take to raise the same quantity?Explanation15 × 8 = 10 × t → t = 12 days.
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Q9 Medium20 men can complete a piece of work in 15 days. How many men are required to complete the same work in 25 days?Explanation20 × 15 = w × 25 → w = 12 men.
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Q10 Medium12 taps can fill a cistern in 20 hours. How long will 16 taps take to fill the same cistern?Explanation12 × 20 = 16 × t → t = 15 hours.
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Q11 MediumTime varies inversely with speed. At 50 km/h a journey takes 6 hours. How long does it take at 60 km/h?Explanation50 × 6 = 60 × t → t = 5 hours.
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Q12 Medium9 men can finish a work in 14 days. How many days will 7 men take?Explanation9 × 14 = 7 × d → d = 18 days.
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Q13 HardIf 8 workers need 21 days to finish a job, how many days will 14 workers need?Explanation8 × 21 = 14 × d → d = 12 days.
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Q14 HardA pipe fills a tank in 40 minutes and another fills it in 60 minutes. How long will both take together?ExplanationCombined rate = 1/40 + 1/60 = 1/24. Together they take 24 minutes.
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DS1 Easy
In a work-rate drill, how many days will 10 men take to finish the job?
Statement I6 men take 18 days to finish the same job.
Statement IIWork is fixed and men × days is constant.
ExplanationStatement I with inverse proportion: 6 × 18 = 10 × d → d = 10.8 days. -
DS2 Medium
What is the time taken at 80 km/h for the same journey?
Statement IAt 60 km/h, the time taken is 4 hours.
Statement IISpeed and time are inversely proportional for a fixed distance.
ExplanationDistance = 240 km. Time at 80 km/h = 3 hours from Statement I alone.
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DS3 Medium
What is x when y = 8?
Statement Ix and y vary inversely.
Statement IIx = 9 when y = 12.
ExplanationTogether: xy = 108, so x = 13.5 when y = 8. -
DS4 Hard
Will fewer workers take more days than 8 workers?
Statement I8 workers finish the job in 15 days.
Statement II12 workers are available for the same job.
ExplanationTogether: 12 workers take 10 days — fewer days, not more. The question is answerable.