18 women complete a work in 24 days and 24 men complete the same work in 15 days. 16 women worked for 3 days and then they left. 20 men worked for the next 2 days, and then they are joined by 16 women. In how many days will they finish the remaining work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(8\frac{2}{5}\)
First find what one woman and one man each do in a day; then the work of any group for any number of days can be added up as a fraction of the whole job.
One day’s work of one person:
18 women take 24 days:
So the job needs \(18\times24=432\) woman-days
One woman does \(\frac{1}{432}\)
24 men take 15 days:
So the job needs \(24\times15=360\) man-days
One man does \(\frac{1}{360}\)
Work done before the two groups join:
16 women for 3 days: \(\displaystyle \frac{16\times3}{432}=\frac{1}{9}\)
20 men for 2 days: \(\displaystyle \frac{20\times2}{360}=\frac{1}{9}\)
Work left \(\displaystyle =1-\frac{1}{9}-\frac{1}{9}=\frac{7}{9}\)
20 men and 16 women together:
One day’s work \(\displaystyle =\frac{20}{360}+\frac{16}{432}=\frac{1}{18}+\frac{1}{27}=\frac{3+2}{54}=\frac{5}{54}\)
Days needed \(\displaystyle =\frac{7}{9}\div\frac{5}{54}=\frac{7}{9}\times\frac{54}{5}=\frac{42}{5}=8\frac{2}{5}\)