UPSC Prelims 2004 Q142: Science & Technology – Quantitative Aptitude
50 men or 80 women can finish a job in 50 days. A contractor deploys 40 men and 48 women
for this work, but after every duration of 10 days, 5 men and 8 women are removed till the work
is completed. The work is completed in
- (a) 45 days
- (b) 50 days
- (c) 54 days
- (d) 62 days
Answer: (b) 50 days
Explanation
Men and women working with removals every ten days
| Step | Work done (in man-days) |
|---|---|
| Total work | 50 men x 50 days = 2,500 man-days; 1 woman = 5/8 man |
| Days 1-10 | 40 men + 48 women = 70 man-equivalents: 700 |
| Days 11-20, 21-30, 31-40 | 60, 50 and 40 man-equivalents: 600 + 500 + 400 |
| After 40 days | 2,200 done; the remaining 300 needs 10 days at 30 man-equivalents |
The job takes 50 days in all: 2,200 man-days are done in the first 40 days and the remaining 300 in the last 10.
Answer: (b) 50 days.
Why each option is right or wrong
- (a) Incorrect. 45 days would need more work done per day.
- (b) CORRECT. The work is completed in 50 days.
- (c) Incorrect. 54 days is more than needed.
- (d) Incorrect. 62 days is more than needed.
Key point
Convert women to men using the given equivalence, then reduce 10 men-equivalents every 10 days.
Remember
The work is completed in 50 days.
Common mistakes
- Forgetting that 5 men and 8 women equal 10 men.
- Using 1 woman = 1 man in the calculation.
- Not stopping the deduction when work is complete.
Exam tip
Find the common unit first: 80 women = 50 men.
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)