2 women and 3 men can do a piece of work in 10 days while 3 women and 2 men can do the same work in 8 days. In how many days can 2 women and 1 man do the work?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(12\frac{1}{2}\) days
A group that finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day. Let one woman do \(w\) and one man \(m\) of the work in a day.
The two equations (from the two groups):
\(\displaystyle 2w+3m=\frac{1}{10}\) (1)
\(\displaystyle 3w+2m=\frac{1}{8}\) (2)
Adding and subtracting (1) and (2):
Adding: \(\displaystyle 5w+5m=\frac{9}{40}\), so \(\displaystyle w+m=\frac{9}{200}\)
Subtracting (1) from (2): \(\displaystyle w-m=\frac{1}{40}=\frac{5}{200}\)
\(\displaystyle w=\frac{7}{200}\), \(\displaystyle m=\frac{2}{200}\)
2 women and 1 man:
One day’s work \(\displaystyle =2\times\frac{7}{200}+\frac{2}{200}=\frac{16}{200}=\frac{2}{25}\)
Days needed \(\displaystyle =\frac{25}{2}=12\frac{1}{2}\)