2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 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?
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4
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8
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6
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Cannot be determined
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None of these
B
Correct answer
Explanation
2 men's 1 day work = 1/6, so 1 man's 1 day work = 1/12. 2 women's 1 day work = 1/9, so 1 woman's 1 day work = 1/18. 3 children's 1 day work = 1/8, so 1 child's 1 day work = 1/24. Work done by 3 women + 4 children in 1 day = 3/18 + 4/24 = 1/6 + 1/6 = 1/3. Remaining work = 2/3. To finish 2/3 work in 1 day, men needed = (2/3)/(1/12) = 8. The key is finding individual work rates first.