A can do a piece of work in 30 days and B in 45 days. They work together for 12 days and then both leave. C alone finishes the remaining work in 8 days. In how many days can C alone do the whole work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and people working together add their one-day work. The part left after A and B stop is the part C does in 8 days.
One-day work of A and B together \(\displaystyle =\frac{1}{30}+\frac{1}{45}=\frac{3+2}{90}=\frac{1}{18}\)
Work done in 12 days \(\displaystyle =12\times\frac{1}{18}=\frac{2}{3}\)
Work left \(\displaystyle =1-\frac{2}{3}=\frac{1}{3}\)
C does \(\frac{1}{3}\) of the work in 8 days, so C does the whole work in \(8\times3=24\) days