A math question. help.?

Question

8 men and 12 boys can do a peice of work in 10 days while 6 men and 8 boys can do the job in 14 days. In how much time can one man do the job.? Please help. How did you solve it?

Answer 1

8 men and 12 boys can do a peice of work in 10 days.

8M + 12B = 1/10

80M + 120B = 1  -> (1)

In one day 80 men and 120B can complete the job.

6 men and 8 boys can do the job in 14 days.

6M + 8B = 1/14

84M + 112B = 1  -> (2)

In one day 84 men and 112B can complete the job.

Solve equation(1) and equation(2).

80M + 120B = 84M + 112B

120B - 112B = 84M - 80M

8B = 4M

2B = 1M

B =1/2 M

Substitute M value in equation (1).

80M + 120(1/2 M) = 1

80M + 60M = 1

140M = 1

M =1/140

A man can do the job in 140 days.