CAPF AC 2021 Q75: General Mental Ability – Quantitative Aptitude
- (a) ₹16,600
- (b) ₹10,000
- (c) ₹21,600
- (d) ₹10,800
Answer: (d) ₹10,800
Explanation
Sharing profit by investment
Given: A, B and C invest ₹7,000, ₹8,000 and ₹12,000; after a year B gets ₹3,200 as profit; find the total profit.
How to think: all three invest for the same time.
So profit is shared in the ratio of the investments.
Use B's share to find the value of one part.
| Step | Working |
|---|---|
| Ratio | 7,000 : 8,000 : 12,000 = 7 : 8 : 12 |
| Total parts | 7 + 8 + 12 = 27 |
| B's 8 parts | ₹3,200 |
| One part | 3,200 ÷ 8 = ₹400 |
| Total profit | 27 × 400 = ₹10,800 |
Check: A gets 7 × 400 = 2,800 and C gets 12 × 400 = 4,800.
2,800 + 3,200 + 4,800 = 10,800.
Answer: (d) ₹10,800.
Why each option is right or wrong
- (a) Incorrect. ₹16,600 is not a multiple of 27 parts of ₹400.
- (b) Incorrect. ₹10,000 would give B about ₹2,963, not ₹3,200.
- (c) Incorrect. ₹21,600 is double the correct amount; it gives B ₹6,400.
- (d) CORRECT. One part is ₹400 and 27 parts make ₹10,800.
Key point
Partnership for equal time: profit ratio = investment ratio. If time differs, use investment × time. Find one part from the known share, then multiply by total parts.
Remember
Same time: profit ratio = capital ratio.
Common mistakes
- Dividing ₹3,200 by 27 instead of by B's 8 parts.
- Adding the investments (₹27,000) and treating that as the profit.
- Forgetting to add all three shares when asked for the total profit.
Exam tip
Educated guess: the total must be a multiple of 27. Among the options only ₹10,800 (27 × 400) and ₹21,600 (27 × 800) qualify, and B's ₹3,200 is 8 × 400.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (ratio and proportion)
- R. S. Aggarwal, Quantitative Aptitude — Partnership