Question

2 men and 5 boys can together finish a work in 4 days while 3 men and 6 boys can finish it in 3 days, find the time taken by one man alone to finish the work,​

Answer 1

Let one man complete the work in 1/x days and one boy completes the work in 1/y days.

Now, 2 men and 5 boys can finish a piece of job in 4 days

⇒ 2x + 5y = 1/4

⇒ 8x + 20y = 1 .........(1)

Also, 3 men and 6 boys finish it in 3 days

⇒ 3x + 6y = 1/3

⇒ 9x + 18y = 1 ........(2)

Now, solving the equations (1) and (2)

We get 1/x = 18 and 1/y = 36

So, Total time taken by one man to complete the job = 18 days