A and B can polish the floors of a building in 25 days. A alone can do \(\frac{1}{3}\) of the job in 15 days. In how many days can B alone polish the floors of the building?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(56\frac{1}{4}\)
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and the one-day work of two people working together is the sum of their one-day works.
A does \(\frac{1}{3}\) of the job in 15 days, so A alone needs \(15\times3=45\) days
One-day work of A and B together \(=\frac{1}{25}\); of A \(=\frac{1}{45}\)
One-day work of B \(\displaystyle=\frac{1}{25}-\frac{1}{45}=\frac{9-5}{225}=\frac{4}{225}\)
B alone needs \(\displaystyle\frac{225}{4}=56\frac{1}{4}\) days