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4 men can complete a piece of work in 3 days. 6 women can complete the same piece of work in 3 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 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 3 days. 6 women can complete the same piece of work in 3 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 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 8

4 men can complete the work in = 3 days

∴ 1 man can complete the work in = 3 × 4 = 12 days

∴ 1 man’s 1 day’s work = 1/12

6 women can complete the work in = 3 days

∴ 1 woman can complete the work in = 3 × 6 = 18 days

∴ 1 woman’s 1 day’s work = 1/18

∴ 3 women’s 1day’s work = 3/18 = 1/6

3 children can complete the work in = 8 days

∴ 1 child can complete the work in = 3 × 8 = 24 days

∴ 1 child’s 1day’s work = 1/24

∴ 4 children’s 1 day’s work = 4/24 = 1/6

∴ Work done by 3 women and 4 children in 1 day = 1/6 + 1/6 = 1/3

∴ Remaining work = 1 – 1/3 = 2/3

In 1 day 1/12 work is done by = 1 man

∴ In 1 day 2/3 work can be done by = 12 × 2/3 = 8 men

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