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2 Men and 3 Women finish a job in 8 days, while 3 men and 2 women finish it in 7 days. How long will 5 men and 4 women take to finish it?

2 Men and 3 Women finish a job in 8 days, while 3 men and 2 women finish it in 7 days. How long will 5 men and 4 women take to finish it? Correct Answer 4 days

Calculation:

Let the efficiency of 1 man and 1 woman for 1 day be M and W

Total work done by 2 men and 3 women in 8 days = 8(2M + 3W)

Total work done by 3 men and 2 women in 7 days = 7(3M + 2W)

Total work is same hence

8(2M + 3W) = 7(3M + 2W)

⇒ M = 2W

⇒ 2M = 4W

Time taken by 5 men and 4 women to finish the job = Total work/(Work done by 5 men and 4 women in 1 day)

⇒ Time taken by 5 men and 4 women to finish the job = 7(3M + 2W) / (5M + 4W) = 28M/7M = 4 days

∴ 5 men and 4 women can complete the work in 4 days

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