Chain Rule— Concepts, Formulas & Shortcuts
- Direct proportion: more of one means more of the other (more men → more work done).
- Inverse proportion: more of one means less of the other (more men → fewer days).
- Universal relation: M₁ × D₁ × H₁ / W₁ = M₂ × D₂ × H₂ / W₂.
- Write the required quantity on the left, then multiply by each ratio in the correct orientation.
- Decide direct or inverse for each factor separately before multiplying anything.
- Sanity-check the answer: if you added men, the number of days must come down.
Chain Rule Practice Questions with Answers
Attempt each question first, then open the explanation. All 18 questions below are free to read and require no signup.
Q1.If 15 men can build a wall in 20 days, how long will 20 men take?
Easy- A12 days
- B15 days
- C18 days
- D25 days
Chain Rule question 1 of 18+Show Answer & Explanation
Answer: B. 15 days
Explanation: Inverse proportion: 15 × 20 = 20 × D → D = 15 days.
Q2.If 8 machines produce 400 items in 5 days, how many items will 12 machines produce in 10 days?
Moderate- A600
- B800
- C1,000
- D1,200
Chain Rule question 2 of 18+Show Answer & Explanation
Answer: D. 1,200
Explanation: 400 × (12/8) × (10/5) = 400 × 1.5 × 2 = 1,200 items.
Q3.If 4 workers earn ₹800 in 5 days, how much will 6 workers earn in 10 days?
Moderate- A₹1,600
- B₹2,000
- C₹2,400
- D₹3,000
Chain Rule question 3 of 18+Show Answer & Explanation
Answer: C. ₹2,400
Explanation: 800 × (6/4) × (10/5) = 800 × 1.5 × 2 = ₹2,400.
Q4.36 men complete a piece of work in 18 days. How many men are needed to complete it in 12 days?
Moderate- A48
- B54
- C60
- D72
Chain Rule question 4 of 18+Show Answer & Explanation
Answer: B. 54
Explanation: 36 × 18 = M × 12 → M = 54 men.
Q5.A car travels 240 km on 16 litres of petrol. How far will it travel on 25 litres?
Easy- A300 km
- B350 km
- C375 km
- D400 km
Chain Rule question 5 of 18+Show Answer & Explanation
Answer: C. 375 km
Explanation: 240 × 25/16 = 375 km.
Q6.If 10 cats kill 10 rats in 10 minutes, how long will 100 cats take to kill 100 rats?
Difficult- A1 minute
- B10 minutes
- C100 minutes
- D1,000 minutes
Chain Rule question 6 of 18+Show Answer & Explanation
Answer: B. 10 minutes
Explanation: Each cat kills one rat in 10 minutes regardless of how many cats there are, so the time stays 10 minutes.
Q7.If 5 pencils cost ₹20, the cost of 12 pencils is:
Easy- A₹40
- B₹44
- C₹48
- D₹52
Chain Rule question 7 of 18+Show Answer & Explanation
Answer: C. ₹48
Explanation: One pencil costs ₹4 → 12 × 4 = ₹48.
Q8.If 6 taps fill a tank in 8 hours, how long will 4 taps take?
Easy- A10 hours
- B12 hours
- C14 hours
- D16 hours
Chain Rule question 8 of 18+Show Answer & Explanation
Answer: B. 12 hours
Explanation: Inverse proportion: 6 × 8 = 4 × T → T = 12 hours.
Q9.If 12 labourers earn ₹9,000 in 6 days, how much will 9 labourers earn in 8 days?
Difficult- A₹7,500
- B₹8,000
- C₹9,000
- D₹10,000
Chain Rule question 9 of 18+Show Answer & Explanation
Answer: C. ₹9,000
Explanation: 9000 × (9/12) × (8/6) = 9000 × 0.75 × 1.333 = ₹9,000.
Q10.A garrison of 500 men has food for 30 days. If 100 men leave, the food will last:
Moderate- A32 days
- B34 days
- C36 days
- D37.5 days
Chain Rule question 10 of 18+Show Answer & Explanation
Answer: D. 37.5 days
Explanation: 500 × 30 = 15,000 man-days → 15,000/400 = 37.5 days.
Q11.If 3 machines produce 180 parts in 4 hours, how many parts will 5 machines produce in 6 hours?
Moderate- A360
- B400
- C450
- D540
Chain Rule question 11 of 18+Show Answer & Explanation
Answer: C. 450
Explanation: 180 × (5/3) × (6/4) = 180 × 1.667 × 1.5 = 450 parts.
Q12.If a wheel makes 240 revolutions in 4 minutes, how many will it make in 7 minutes?
Easy- A360
- B400
- C420
- D480
Chain Rule question 12 of 18+Show Answer & Explanation
Answer: C. 420
Explanation: 60 revolutions per minute → 60 × 7 = 420.
Q13.If 3 books cost ₹150, the cost of 8 books is:
Easy- A₹350
- B₹400
- C₹450
- D₹500
Chain Rule question 13 of 18+Show Answer & Explanation
Answer: B. ₹400
Explanation: One book costs ₹50 → 8 × 50 = ₹400.
Q14.If 10 men build a wall in 12 days, 15 men will take:
Easy- A6 days
- B8 days
- C9 days
- D10 days
Chain Rule question 14 of 18+Show Answer & Explanation
Answer: B. 8 days
Explanation: 10 × 12 = 120 man-days → 120/15 = 8 days.
Q15.If a train covers 180 km in 3 hours, how far will it go in 5 hours at the same speed?
Easy- A240 km
- B270 km
- C300 km
- D320 km
Chain Rule question 15 of 18+Show Answer & Explanation
Answer: C. 300 km
Explanation: Speed = 60 km/h → 60 × 5 = 300 km.
Q16.Food for 200 soldiers lasts 40 days. If 50 more join, it will last:
Moderate- A28 days
- B30 days
- C32 days
- D35 days
Chain Rule question 16 of 18+Show Answer & Explanation
Answer: C. 32 days
Explanation: 200 × 40 = 8,000 man-days → 8,000/250 = 32 days.
Q17.If 5 printers print 500 pages in 10 minutes, how many pages will 8 printers print in 20 minutes?
Moderate- A1,200
- B1,400
- C1,600
- D2,000
Chain Rule question 17 of 18+Show Answer & Explanation
Answer: C. 1,600
Explanation: 500 × (8/5) × (20/10) = 500 × 1.6 × 2 = 1,600 pages.
Q18.If 9 workers can finish a job in 15 days, how many workers are needed to finish it in 9 days?
Moderate- A12
- B15
- C18
- D20
Chain Rule question 18 of 18+Show Answer & Explanation
Answer: B. 15
Explanation: 9 × 15 = 135 worker-days → 135/9 = 15 workers.
Chain Rule — Frequently Asked Questions
How do I decide between direct and inverse proportion?+
Ask what happens to the answer if the quantity increases while everything else stays fixed. More machines produce more items (direct), but more machines need fewer days (inverse).
Why do 100 cats take the same 10 minutes to kill 100 rats as 10 cats take for 10 rats?+
Because both the number of cats and the amount of work scale by the same factor of 10. The two effects cancel, leaving the time unchanged — a classic trap question.
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