A contractor falls behind — Time & Work Aptitude Question
A contractor falls behind: A contractor undertakes to finish a job in 40 days with 100 men. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 135 seconds
Question
A contractor undertakes to finish a job in 40 days with 100 men. After 30 days only two-thirds of the work is done. How many additional men must he employ to finish on time?
Options
- 25
- 50
- 75
- 100
Show the answer and the worked solution
Correct answer: B. 50
Worked solution
- Two-thirds of the work took 100 × 30 = 3,000 man-days, so the whole job is 4,500 man-days.
- Remaining = 1,500 man-days in 10 days → 150 men needed.
- Additional men = 150 − 100 = 50.
Answer: 50.
The idea
Scale the observed man-days to the whole job, then divide the remainder by the days left. The question asks for the extra men, not the new total.
Shortcut. 100 men do a third of the job in 15 days; doing the last third in 10 days needs 100 × 15/10 = 150 men, so 50 more.
Common trap. 100 — doubling the crew on the feeling that the last third must go twice as fast; it must go 1.5 times as fast (a third in 10 days, not 15).