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

$$=$$>  Total work = 34(5M+8W) = 170M + 272W

Total work done by 4 men and 18 women in 28 days

$$=$$>  Total work = 28(4M+18W) = 112M + 504W

$$\therefore\ $$170M + 272W = 112M + 504W

$$=$$>  58M = 232W

$$=$$>  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 = $$\frac{952W}{3M+5W}=\frac{952W}{3\left(4W\right)+5W}=\frac{952W}{17W}=56$$ days

Hence, the correct answer is Option A