Three men can complete a work in 6 days and 5 women can complete the same work in 18 days. In how many days can 4 men and 10 women together complete the same work?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3
The whole work is the same in both cases, so it is measured in man-days and woman-days: the number of workers times the days they take.
Work \(=3\times6=18\) man-days, so one man does \(\displaystyle\frac{1}{18}\) of the work in a day
Work \(=5\times18=90\) woman-days, so one woman does \(\displaystyle\frac{1}{90}\) of the work in a day
4 men and 10 women in a day: \(\displaystyle\frac{4}{18}+\frac{10}{90}=\frac{2}{9}+\frac{1}{9}=\frac{1}{3}\) of the work
Time for the whole work \(=3\) days