5 men and 8 women can complete a task in 34 days, whereas 4 men and 18 women can complete the same task in 28 days. In how many days can the same task be completed by 3 men and 5 women?
Let the work done by 1 man in 1 day = M
work done by 1 woman in 1 day = W
Total work done by 5 men and 8 women in 34 days
$$=$$>Â Total work = 34(5M+8W) = 170M + 272W
Total work done by 4 men and 18 women in 28 days
$$=$$>Â Total work = 28(4M+18W) = 112M + 504W
$$\therefore\ $$170M + 272W = 112M + 504W
$$=$$>Â 58M = 232W
$$=$$>Â M = 4W
Total work = 170M + 272W = 170(4W) + 272W = 680W + 272W = 952W
Number of days required for 3 men and 5 women to complete the task =Â $$\frac{952W}{3M+5W}=\frac{952W}{3\left(4W\right)+5W}=\frac{952W}{17W}=56$$ days
Hence, the correct answer is Option A
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