More men join partway — Time & Work Aptitude Question
More men join partway: 12 men undertake a work expected to take 20 days. After 8 days, 4 more men join. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
12 men undertake a work expected to take 20 days. After 8 days, 4 more men join. In how many days in total is the work finished?
Options
- 16 days
- 17 days
- 18 days
- 19 days
Show the answer and the worked solution
Correct answer: B. 17 days
Worked solution
- Total work = 240 man-days.
- In 8 days: 12 × 8 = 96 done, leaving 144.
- With 16 men: 144 ÷ 16 = 9 more days.
- Total = 8 + 9 = 17 days.
Answer: 17 days.
The idea
Track man-days used and remaining. The answer is the total elapsed time, so remember to add the first stretch back on.
Shortcut. The last 12 days' work for 12 men takes 16 men 12 × 12/16 = 9 days, so the total is 8 + 9 = 17.
Common trap. 16 days — cutting the remaining 12 days by a third because the crew grew by a third; a third more men cuts time by a quarter, to 9 days.