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?

56

5M + 8W = 34 days,

170M + 272W    ..(1)    (Multiplied by 34 to get in one day),

4M + 18W = 28 days,

112M + 504W    ..(2)    (Multiplied by 28 to get in one day),

Now (1) - (2)

⇒ 58M = 232W

⇒ M : W = 232 : 58 = 4 : 1  (Efficiency) 

⇒ Putting in (1) to find total work,

⇒ [170(4) + 232(1)] = 680 + 272 = 952 units,

⇒ Time required by 3 Men and 5 Women to complete the total work = \(\frac{952}{3(4)+5(1)}\) = \(\frac{952}{17}\) = 56 days,     ..(\(\frac{Work}{Efficiency}\) = Time)