X, Y and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24
A person who finishes a work in \(n\) days does \(\frac{1}{n}\) of it in a day, and the day’s work of people working together adds up. Here X and Y each take 16 days alone, so Z’s share is what is left of the three together.
X, Y and Z together in one day: \(\frac{1}{6}\)
X and Y in one day: \(\frac{1}{16}+\frac{1}{16}=\frac{1}{8}\)
Z in one day: \(\displaystyle\frac{1}{6}-\frac{1}{8}=\frac{4-3}{24}=\frac{1}{24}\)
So Z alone needs 24 days