Question

2 men and 5 women can do a piece of work in 4 days while one man and one woman can finish it in 12 days. How long would it take for 1 man to do the work

Answer 1

Let one man do the work alone in m days. 
Let one boy do the work alone in b days.

In one day 1m part of the work is done by 1 man and 
in one day 1b part of the work is done by 1 boy.
 
Now by given condition we have 
2×1m+3×1b=110  ⋯(A)
(work done by 2 men and 3 boys in one day) 

We also have 
3×1m+2×1b=18  ⋯(B) 

Solving above two equations we get 
1b=1100 and 1m=7200
 
We are asked to find how many days will 2men and 1 boy take. 
First we find out work completed in one day by 2 men and 1 boy 
=2×7200+1100=8100=112.5
 
Thus the work will be completed in 12.5days