3 men and four boys can do

Question

3 men and 4 boys can do a piece of work in 14 days while 4 men and 6 boys do the same work in 10 days. how long would it take one man to finish the same work?

Answer 1

Assume one man can do a piece of work in d days. Two men can do the same piece of work in d/2 days, 3 men in d/3 and so on. Similarly, if 1 boy can do the work in e days, 3 boys can do the work in e/3 days. So m men can do an amount of work in d/m days and b boys can do the work in e/b days.
d/3+e/4=14 and d/4+e/6=10.
Multiply the equations by 12: 4d+3e=168 and 3d+2e=120.
We can eliminate e by doubling the first of these new eqns and trebling the second: 8d+6e=336 and 9d+6e=360. Subtract the latter from the former to get d=24.
So one man can do the work in 24 days. (Incidentally, so can one boy!)