Question

3 men and 4 women can complete a job in
10 days. 24 men and 2 women can complete it in
2 days. Find the time taken by 11 men and
3 women to complete it.​

Answer 1

While solving all “Time and Work” problems, estimating the Total Work is the key.

Here in all the three cases, the work done is same. But it is done by different combination of workforces.

4 Men and 6 Women take 8 days. So TOTAL WORK = 32 MD + 48 WD (where MD= Mandays, & WD = Womandays, a unit of work) ……(eqn1)

3 Men and 7 Women take 10 days. So, TOTAL WORK = 30 MD + 70 WD …. (eqn2)

Equating the total work,

32 MD + 48 WD = 30 MD + 70 WD

=> 2 MD = 22 WD

=> 1 MD = 11 WD

So, replacing man days in eqn2,

TOTAL WORK = 400 WD

Now, 10 women will complete 10 WD of work in one day.

To complete 400 WD of work,

Time needed = (400 WD)/(10 WD) = 40 Days (Answer)