Pariksha SaathiQuantitative Aptitude
Chain Rule: Practice Questions with Answers
14 practice questions on Chain Rule, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.1
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
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Answer: 24 days
Solution:
- More men → fewer days (inverse proportion): days = 36 × 18 / 27.
- = 648 / 27 = 24 days.
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Q.2
The cost of 8 pens equals the cost of 6 pencils. If the cost of 10 pencils is ₹150, find the cost of 20 pens.
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Answer: ₹225
Solution:
- Cost of 1 pencil = 150 / 10 = ₹15, so the cost of 6 pencils = 6 × 15 = ₹90.
- The cost of 8 pens equals this: 8 pens = ₹90, so 1 pen = 90/8 = ₹11.25.
- Cost of 20 pens = 20 × 11.25 = ₹225.
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Q.3
If 6 men can earn ₹9,000 in 5 days, how much will 8 men earn in 10 days, at the same daily wage rate per man?
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Answer: ₹24,000
Solution:
- Earnings scale up directly with both the number of men and the number of days.
- New earnings = 9,000 × (8/6) × (10/5) = 9,000 × (4/3) × 2
- = 9,000 × 8/3 = ₹24,000.
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Q.4
If 15 workers can build a wall in 12 days working 8 hours a day, how many days will 18 workers take to build the same wall working 10 hours a day?
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Answer: 8 days
Solution:
- More workers → fewer days (inverse): multiply by 15/18.
- More hours per day → fewer days (inverse): multiply by 8/10.
- Days = 12 × (15/18) × (8/10) = 12 × (5/6) × (4/5) = 8 days.
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Q.5
A garrison of 500 men has food that will last 30 days. After 10 days, 100 more men join. For how many more days will the remaining food last?
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Answer: ≈ 16.67 days (16 days and 16 hours)
Solution:
- Total food stock = 500 × 30 = 15,000 "man-days".
- Used in the first 10 days = 500 × 10 = 5,000 man-days. Remaining = 15,000 − 5,000 = 10,000 man-days.
- New headcount = 500 + 100 = 600. Remaining days = 10,000 / 600 ≈ 16.67 days.
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Q.6
A car covers a certain distance in 5 hours at a speed of 60 km/hr. If the speed is increased to 75 km/hr, find the time taken to cover the same distance.
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Answer: 4 hours
Solution:
- The distance stays fixed, and speed and time are inversely proportional: time = (5 × 60) / 75.
- = 300 / 75 = 4 hours.
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Q.7
If 20 men can build a 50 m long wall in 12 days, how many days will 15 men take to build a 75 m long wall (at the same rate of work)?
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Answer: 24 days
Solution:
- Chain the ratios: fewer men → more days (inverse, multiply by 20/15); more wall to build → more days (direct, multiply by 75/50).
- Days = 12 × (20/15) × (75/50) = 12 × (4/3) × (3/2)
- = 12 × 2 = 24 days.
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Q.8
20 workers can build a wall in 15 days working 6 hours a day. How many days will 15 workers take to build the same wall working 8 hours a day?
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Q.9
A ship has provisions for 400 passengers for 60 days. After 15 days, 100 passengers leave the ship. For how many more days will the remaining food last?
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Answer: 60 days. Stock = 24,000 man-days; used = 6,000; remaining = 18,000 ÷ 300 passengers.
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Q.10
If 25 men can build a 40 m long wall in 16 days, how many days will 20 men take to build a 60 m long wall?
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Q.11
15 workers can complete a task in 8 days working 6 hours a day. How many days will 12 workers take, working 10 hours a day?
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Q.12
24 men can complete a job in 20 days. In how many days will 30 men complete the same job?
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Q.13
The cost of 12 notebooks is ₹180. Find the cost of 20 notebooks.
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Q.14
If 5 men can earn ₹6,000 in 8 days, how much will 10 men earn in 6 days, at the same daily wage rate?
How these questions were made
Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-03.