X, Y and Z together can complete a work in 6 days. X alone, as well as Y alone, can do the same work in 16 days. In how many days can Z alone complete the same work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24
Work is added through one day’s work: a person who finishes the work in \(n\) days does \(\frac{1}{n}\) of it in a day, and the one-day works of people working together add up. Z’s share is what is left after taking away X’s and Y’s.
X, Y and Z together in one day: \(\frac{1}{6}\)
X and Y in one day: \(\displaystyle \frac{1}{16}+\frac{1}{16}=\frac{1}{8}\)
Z in one day: \(\displaystyle \frac{1}{6}-\frac{1}{8}=\frac{4-3}{24}=\frac{1}{24}\)
Z alone finishes the work in 24 days