Women and children — Time & Work Aptitude Question
Women and children: 10 women can complete a work in 7 days and 10 children take 14 days. Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
10 women can complete a work in 7 days and 10 children take 14 days. How long will 5 women and 10 children take together?
Options
- 3.5 days
- 5 days
- 7 days
- 10 days
Show the answer and the worked solution
Correct answer: C. 7 days
Worked solution
- One woman = 1/70 per day; one child = 1/140 per day.
- 5 women + 10 children = 5/70 + 10/140 = 1/14 + 1/14 = 2/14 = 1/7.
- Time = 7 days.
Answer: 7 days.
The idea
Reduce to the rate of a single worker of each kind, then scale and add. Halving the women and keeping the children happens to balance out here.
Shortcut. 5 women are half a 7-day crew, so alone they need 14 days — the same as the 10 children. Two 14-day teams together take 7 days.
Common trap. 3.5 days — halving 7 on the reflex that two groups halve the time; that holds only if each group alone takes 7 days, and here each takes 14.