A can do a piece of work in 24 days and B in 40 days. They work together for 12 days and then both leave. C alone finishes the remaining work in 6 days. In how many days can C alone do the whole work?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30 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 6 days.
One-day work of A and B together \(\displaystyle =\frac{1}{24}+\frac{1}{40}=\frac{5+3}{120}=\frac{1}{15}\)
Work done in 12 days \(\displaystyle =12\times\frac{1}{15}=\frac{4}{5}\)
Work left \(\displaystyle =1-\frac{4}{5}=\frac{1}{5}\)
C does \(\frac{1}{5}\) of the work in 6 days, so C does the whole work in \(6\times5=30\) days