UPSC Prelims 2008 Q4: Science & Technology – Quantitative Aptitude
Carpenter A can make a chair in 6 hours, carpenter B in 7 hours and carpenter C in 8 hours. If
each carpenter works for 8 hours per day, how many chairs will be made in 21 days?
- (a) 61
- (b) 67
- (c) 73
- (d) 79
Answer: (c) 73
Explanation
Counting chairs made by three carpenters over 21 days
Carpenters A, B, and C make chairs at different individual rates, working 8 hours per day.
| Carpenter | Rate | Chairs per 8-hour day |
|---|---|---|
| A | 1 chair / 6 hours | 8/6 = 4/3 chairs/day |
| B | 1 chair / 7 hours | 8/7 chairs/day |
| C | 1 chair / 8 hours | 8/8 = 1 chair/day |
Multiplying each carpenter's daily rate by 21 days of work:
| Step | Calculation over 21 days |
|---|---|
| A's total | 21 × 4/3 = 28 chairs |
| B's total | 21 × 8/7 = 24 chairs |
| C's total | 21 × 1 = 21 chairs |
| Combined total | 28 + 24 + 21 = 73 chairs |
| Why 21 days | 21 is divisible by both 3 and 7, so the fractional daily rates resolve to whole numbers |
Answer: (c) 73.
Why each option is right or wrong
- (a) Incorrect. 61 undercounts the correct combined total.
- (b) Incorrect. 67 also undercounts the correct total.
- (c) CORRECT. A makes 28, B makes 24, C makes 21 chairs over 21 days — totaling 73.
- (d) Incorrect. 79 overstates the correct combined total.
Key point
Over 21 days at 8 hours/day: Carpenter A makes 28 chairs, B makes 24, C makes 21 — a combined total of 73 chairs.
Remember
Carpenters A (6h/chair), B (7h/chair), C (8h/chair), 8h/day for 21 days: combined total = 73 chairs.
Common mistakes
- Miscalculating each carpenter's daily chair rate (8 hours divided by their individual completion time).
- Forgetting that 21 days was specifically chosen to make the fractional rates resolve cleanly.
- Making an arithmetic error while summing the three carpenters' 21-day totals.
Exam tip
For 'work rate × time' problems with multiple workers, calculate each worker's rate separately, then sum their individual totals.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Work)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Time and Work)