A man, a woman and a boy finish work together in 6 days. Working alone, man…
2025
A man, a woman and a boy finish work together in 6 days. Working alone, man takes 10 days, woman takes 24 days then the ratio of working capacity of a man, a woman and a boy is?
- A.
12:5:2
- B.
12:5:3
- C.
5:12:30
- D.
5:12:40
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Correct answer: B
Answer: 12 : 5 : 3
Let the boy take b days. Then daily work rates are:
Man: 1/10 per day
Woman: 1/24 per day
Boy: 1/b per day
Together they complete the work in 6 days, so combined rate = 1/6 per day.
Compute the boy's rate: 1/b = 1/6 - (1/10 + 1/24) = 20/120 - 17/120 = 3/120 = 1/40, so b = 40.
Thus the daily rates are 1/10 : 1/24 : 1/40. Clearing denominators by multiplying each term by 120 gives 12 : 5 : 3.