CAPF AC 2021 Q53: General Mental Ability – Quantitative Aptitude
A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?
- (a) 35 2⁄7 days
- (b) 37 1⁄7 days
- (c) 34 2⁄7 days
- (d) 33 2⁄7 days
Answer: (c) 34 2⁄7 days
Explanation
Work done by pairs
Given: A and B together finish a job in 20 days, B and C in 30 days, A and C in 24 days; find the days A alone needs.
How to think: add the three pair rates.
Each person is counted twice, so halve the total to get all three together.
Then remove the pair that does not contain A.
| Step | Working |
|---|---|
| One-day work of the pairs | A+B = 1/20, B+C = 1/30, A+C = 1/24 |
| Add them | 2(A+B+C) = 6/120 + 4/120 + 5/120 = 15/120 = 1/8 |
| All three together | A+B+C = 1/16 |
| A alone | 1/16 − 1/30 = 15/240 − 8/240 = 7/240 |
| Days for A | 240/7 = 34 2⁄7 days |
Answer: (c) 34 2⁄7 days.
Why each option is right or wrong
- (a) Incorrect. 35 2⁄7 days is 247/7, but the work rate of A gives exactly 240/7.
- (b) Incorrect. 37 1⁄7 days is too long; A's rate of 7/240 per day finishes sooner.
- (c) CORRECT. A does 7/240 of the job a day, so A needs 240/7 = 34 2⁄7 days.
- (d) Incorrect. 33 2⁄7 days is 233/7, which does not match 240/7.
Key point
Pairs given: add the three rates and halve to get A+B+C. Then A = (A+B+C) − (B+C). Here A+B+C = 1/16 and A = 7/240.
Remember
A = (sum of pair rates ÷ 2) − (B+C).
Common mistakes
- Forgetting to halve the sum of the three pair rates before subtracting.
- Subtracting the wrong pair; to find A you must remove B and C.
- Adding the days (20 + 30 + 24) instead of adding the one-day work.
Exam tip
Educated guess: A works with B in 20 days, so A alone must take more than 20 days. All four options pass that test, so here the full working is needed; use 120 as the common base.
Sources
- NCERT Class VIII Mathematics — Direct and Inverse Proportions (time and work)
- R. S. Aggarwal, Quantitative Aptitude — Time and Work