Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How many days will a woman take to do the job, if she works alone on it?
Answers
Please see the attachment
If the woman works alone on it, she will take 54 days to complete it.
Let the amount of work done by the man in one day be ‘m′ and the amount of work done by the woman in one day be ‘w′.
Given that, Four men and three women can do a job in 6 days,
So, 4 men and 3 women will do (4m + 3w) amount of work in one day.
Also, it is given that, they (4 men and 3 women) complete the entire work in 6 days. So, the work done in one day will be 1/6.
We can represent these above sentences as:
4m + 3w = 1/6
3w = (1/6) - 4m
6w = (1/3) - 8m ...(1) [Multiplying by 2 on both sides.]
Similarly, it is stated that five men and six women work on the same job, the work gets completed in 4 days. Thus,
5m + 6w = 1/4 ...(2)
Replacing the value of 6w from (1) in (2), we get:
5m + (1/3) - 8m = 1/4
⇒ 8m - 5m = 1/3 - 1/4
⇒ 3m = 1/12
⇒ m = 1/(12×3) = 1/36
So, a man does (1/36)th of the work in one day. Hence he will take 36 days to do the work.
Replacing the value of m in (1), we get:
6w = (1/3) - 8(1/36)
⇒ 6w = 1/9
⇒ w = 1/(9×6) = 1/54
So, a woman does (1/54)th of the work in one day. Hence she will take 54 days to do the entire work.