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?
Answer & explanation
Correct answer: option 3
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)