A man, a woman and a boy can do a work in 6, 9 and 18 days respectively. How many boys must assist one man and one woman to do the work in 1 day?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 13
A person who finishes a work in \(n\) days does \(\frac{1}{n}\) of it in one day. To finish in 1 day, the one-day shares of the man, the woman and the boys must add up to the whole work.
One day’s work: man \(\frac{1}{6}\), woman \(\frac{1}{9}\), one boy \(\frac{1}{18}\)
Man and woman together in one day: \(\displaystyle \frac{1}{6}+\frac{1}{9}=\frac{3+2}{18}=\frac{5}{18}\)
Work left for the boys: \(\displaystyle 1-\frac{5}{18}=\frac{13}{18}\)
Each boy does \(\frac{1}{18}\) a day, so 13 boys are needed