A can do a piece of work in 15 days and B can do it in 21 days. They work together for 5 days; then B leaves and A continues alone. After 3 more days C joins A, and the work is completed in 2 more days. In how many days can C alone do the work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 21 days
The work done in the separate stretches adds up to the whole work, so the part C does in the last 2 days gives C's one-day work.
A and B for 5 days \(\displaystyle =5\left(\frac{1}{15}+\frac{1}{21}\right)=5\times\frac{7+5}{105}=\frac{60}{105}=\frac{4}{7}\)
A for the next 5 days (3 days alone + 2 days with C) \(\displaystyle =5\times\frac{1}{15}=\frac{1}{3}\)
Work done by C in 2 days \(\displaystyle =1-\frac{4}{7}-\frac{1}{3}=\frac{21-12-7}{21}=\frac{2}{21}\)
C's one-day work \(\displaystyle =\frac{1}{21}\)
C alone can do the work in 21 days.