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4 men can complete a piece of work in 5 days. 5 women can complete the same piece of work in 8 days, whereas 8 children can complete the same piece of work in 10 days. 3 women and 6 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?

4 men can complete a piece of work in 5 days. 5 women can complete the same piece of work in 8 days, whereas 8 children can complete the same piece of work in 10 days. 3 women and 6 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required? Correct Answer 17

4 men can complete the work in = 5 days

∴ 1 man can complete the work in = 5 × 4 = 20 days

∴ 1 man’s 1 day’s work = 1/20

5 women can complete the work in = 8 days

∴ 1 woman can complete the work in = 8 × 5 = 40 days

∴ 1 woman’s 1 day’s work = 1/40

∴ 3 women’s 1day’s work = 3/40

8 children can complete the work in = 10 days

∴ 1 child can complete the work in = 10 × 8 = 80 days

∴ 1 child’s 1day’s work = 1/80

∴ 6 children’s 1 day’s work = 6/80 = 3/40

∴ work done by 3 women and 6 children in 1 day = 3/40 + 3/40 = 3/20

∴ remaining work = 1 – 3/20 = 17/20

Let, x men will be required.

According to the question,

⇒ x × 1/20 = 17/20

⇒ x = 17

∴ 17 men would be required

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