Nine boys can complete a work in 360 days, 18 men can complete the same work in 72 days and 12 women can complete it in 162 days. In how many days, can 4 men, 12 women and 10 boys together, complete the work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 81
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and the one-day work of people working together is added. So the one-day work of one boy, one man and one woman is found first.
One person’s time for the whole work:
1 boy: \(9\times360=3240\) days
1 man: \(18\times72=1296\) days
1 woman: \(12\times162=1944\) days
One-day work of the group (4 men, 12 women, 10 boys; LCM of 1296, 1944 and 3240 is 19440):
4 men: \(\displaystyle\frac{4}{1296}=\frac{60}{19440}\)
12 women: \(\displaystyle\frac{12}{1944}=\frac{120}{19440}\)
10 boys: \(\displaystyle\frac{10}{3240}=\frac{60}{19440}\)
Together: \(\displaystyle\frac{60+120+60}{19440}=\frac{240}{19440}=\frac{1}{81}\)
The group does \(\frac{1}{81}\) of the work a day, so it finishes the work in 81 days.