Pariksha SaathiChain Rule (Compound Proportion) Questions with Solutions
Chain Rule questions involve three or more related quantities at once (workers, days, hours; or men and days) — the method is to set up a direct or inverse proportion for each pair and chain them together, not to guess which way to multiply. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- Identify whether each pair of quantities is DIRECTLY proportional (both increase together, like cost and quantity) or INVERSELY proportional (one increases as the other decreases, like workers and days for a fixed job).
- More workers → fewer days needed (inverse). More hours per day → fewer days needed (inverse). More work to do → more days needed (direct).
- Set up the unknown as: new value = old value × (ratio that makes sense for each relationship) — for an inverse relationship, the ratio is old/new; for a direct relationship, it’s new/old.
- Chain every relevant ratio together in one single equation rather than solving pair by pair — this avoids rounding errors and mixed-up intermediate steps.
Worked examples
1. 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?
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.
Answer: 8 days
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.
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.
Answer: ₹225
3. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Solution
- More men → fewer days (inverse proportion): days = 36 × 18 / 27.
- = 648 / 27 = 24 days.
Answer: 24 days
4. 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.
Solution
- The distance stays fixed, and speed and time are inversely proportional: time = (5 × 60) / 75.
- = 300 / 75 = 4 hours.
Answer: 4 hours
Try these yourself
Identify each relationship as direct or inverse first, then check against the answer.
1. 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?
Answer: 15 days
2. The cost of 12 notebooks is ₹180. Find the cost of 20 notebooks.
Answer: ₹300
3. 24 men can complete a job in 20 days. In how many days will 30 men complete the same job?
Answer: 16 days
Where this comes up
Chain Rule (Compound Proportion) is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and frequently combines with Time and Work.
Practice more Chain Rule questions
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