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 Easy
If 6 workers finish a job in 12 days, 8 workers will finish in:
Explanation6 × 12 = 8 × d → d = 9 days. -
Q2 Easy
A car at 60 km/h takes 5 hours. At 75 km/h it takes:
Explanation60 × 5 = 75 × t → t = 4 hours. -
Q3 Medium
If 15 pumps fill a tank in 8 hours, 10 pumps will take:
Explanation15 × 8 = 10 × t → t = 12 hours. -
Q4 Easy
x varies inversely with y. If x = 12 when y = 5, x when y = 10:
Explanationxy = 60. x = 60/10 = 6. -
Q5 Easy
If 4 men do work in 18 days, 6 men do it in:
Explanation4 × 18 = 6 × d → d = 12. -
Q6 Easy
Speed doubled, time for same distance becomes:
ExplanationInverse relation: time halves. -
Q7 Medium
20 workers, 15 days. How many workers for 25 days?
Explanation20 × 15 = w × 25 → w = 12.
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Q8 Medium
If m₁d₁ = m₂d₂, 9 men × 14 days = 7 men × d days. d =
Explanation126 = 7d → d = 18. -
Q9 Hard
A pipe fills tank in 40 min. Another fills in 60 min. Together, time is:
ExplanationCombined rate 1/40 + 1/60 = 1/24 → 24 min. -
Q10 Easy
If x × y = 72 and y increases from 6 to 9, x becomes:
Explanationx = 72/9 = 8. -
Q11 Medium
12 taps fill a cistern in 20 hours. 16 taps will take:
Explanation12 × 20 = 16 × t → t = 15. -
Q12 Easy
If 5 machines produce in 8 hours, 10 machines produce in:
Explanation5 × 8 = 10 × t → t = 4. -
Q13 Medium
Time varies inversely with speed. 50 km/h → 6 hours. 60 km/h →
Explanation50 × 6 = 60 × t → t = 5. -
Q14 Hard
If 8 workers need 21 days, 14 workers need:
Explanation168 = 14 × d → d = 12.
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DS1 Easy
How many days will 10 men take?
Statement I6 men take 18 days.
Statement IIWork is fixed and men × days is constant.
Explanation6 × 18 = 10 × d → d = 10.8 days from I alone if constant product. -
DS2 Medium
What is the time at 80 km/h?
Statement IAt 60 km/h, time is 4 hours for the same distance.
Statement IISpeed and time are inversely proportional.
ExplanationDistance = 240 km. Time at 80 = 3 hours.
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DS3 Medium
What is x when y = 8?
Statement Ix and y vary inversely.
Statement IIx = 9 when y = 12.
Explanationxy = 108. x = 13.5 when y = 8. -
DS4 Hard
Will fewer workers take more days?
Statement I8 workers finish in 15 days.
Statement II12 workers are available.
Explanation12 workers take 10 days — fewer days, not more.