2 men and 3 women together can complete a piece of work in 8 days. 1 man and 2 boys together complete the work in 16 days. 3 women and 2 boys together can complete the work in 12 days. In how many days 2 men, 3 women and 4 boys together can complete the work?
2 men and 3 women together can complete a piece of work in 8 days. 1 man and 2 boys together complete the work in 16 days. 3 women and 2 boys together can complete the work in 12 days. In how many days 2 men, 3 women and 4 boys together can complete the work? Correct Answer 72/13 days
Let M, W and B be the number of days taken by a man, a woman, and a boy each working alone to complete the work.
2 men and 3 women together can complete a piece of work in 8 days.
⇒ 2/M + 3/W = 1/8 ----(1)
1 man and 2 boys together complete the work in 16 days.
⇒ 1/M + 2/B = 1/16 ----(2)
3 women and 2 boys together can complete the work in 12 days.
⇒ 3/W + 2/B = 1/12 ----(3)
On multiplying equation 2 by 2 and then subtracting from equation 1,
⇒ 3/W = 4/B ----(4)
Putting value in equation 3,
⇒ 6/B = 1/12 and 9/W = 1/6
⇒ B = 72 days and W = 54 days
From equation 1,
⇒ M = 144/5 days
∴ 2 men, 3 women and 4 boys together can complete the work in = 72/13 days
