CAPF AC 2022 Q33: General Mental Ability – Quantitative Aptitude
Suppose A and B can complete a work together in 10 days. If B alone can complete the work in 15 days, then in how many days can A alone finish the work?
- (a) 20 days
- (b) 24 days
- (c) 25 days
- (d) 30 days
Answer: (d) 30 days
Explanation
Work done by one of two workers
Given: A and B together finish a work in 10 days; B alone finishes it in 15 days; find the days A alone needs.
How to think: work with one day's work.
A's share is what is left after removing B's share from the joint work.
| Step | Working |
|---|---|
| A and B in one day | 1/10 |
| B in one day | 1/15 |
| A in one day | 1/10 − 1/15 = 3/30 − 2/30 = 1/30 |
| Days for A alone | 30 days |
Check: 1/30 + 1/15 = 1/30 + 2/30 = 3/30 = 1/10.
Answer: (d) 30 days.
Why each option is right or wrong
- (a) Incorrect. With 20 days for A, the two together would finish in about 8.6 days.
- (b) Incorrect. With 24 days for A, the two together would take about 9.2 days.
- (c) Incorrect. 25 days comes from adding 10 and 15, which is not how rates combine.
- (d) CORRECT. A does 1/30 of the work a day, so A needs 30 days.
Key point
Rates add, days do not. A's rate = joint rate − B's rate. Shortcut: A alone = (10 × 15) ÷ (15 − 10) = 30 days.
Remember
A alone = product ÷ difference = 150 ÷ 5 = 30.
Common mistakes
- Subtracting the days (15 − 10 = 5) instead of the one-day work.
- Adding the days 10 and 15 to get 25 days for A alone.
- Expecting A to be faster than B; here A is the slower worker.
Exam tip
Educated guess: use the product over difference rule: 10 × 15 = 150, and 15 − 10 = 5, so 150 ÷ 5 = 30.
Sources
- NCERT Class VIII Mathematics — Direct and Inverse Proportions (time and work)
- R. S. Aggarwal, Quantitative Aptitude — Time and Work