Men, women and hours — Time & Work Aptitude Question
Men, women and hours: 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 150 seconds
Question
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, if 3 women do as much work as 2 men?
Options
- 20
- 25
- 30
- 36
Show the answer and the worked solution
Correct answer: C. 30
Worked solution
- Total work = 15 × 21 × 8 = 2,520 man-hours.
- 3 women ≡ 2 men, so 21 women ≡ 14 men.
- Daily output = 14 × 6 = 84 man-hours.
- Days = 2,520 ÷ 84 = 30 days.
Answer: 30 days.
The idea
Convert the workforce into one unit first, then work in that unit's hours throughout. Attempting to convert at the end mixes incompatible quantities.
Shortcut. 21 women = 14 men. Days = 21 × 15/14 × 8/6; 21/14 = 3/2 and 15 × 8/6 = 20, so 3/2 × 20 = 30.
Common trap. 20 — counting the 21 women as 21 men (21 × 15/21 × 8/6 = 20); they are worth only 14 men.