A and B can do a piece of work in 10 days and 15 days respectively. They worked together for 5 days, then B left the work and A alone did the remaining work. The whole work got completed in:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(6\frac{2}{3}\) days
Count the work as a fraction of the whole job: a person who needs \(n\) days alone does \(\frac{1}{n}\) of the work in one day, and the shares of people working together add up.
A's one-day work \(=\frac{1}{10}\); B's one-day work \(=\frac{1}{15}\)
Together in one day: \(\displaystyle\frac{1}{10}+\frac{1}{15}=\frac{3+2}{30}=\frac{1}{6}\) of the work
Done together in 5 days: \(\displaystyle5\times\frac{1}{6}=\frac{5}{6}\); left for A: \(\frac{1}{6}\)
Time A takes for it: \(\displaystyle\frac{1}{6}\div\frac{1}{10}=\frac{10}{6}=1\frac{2}{3}\) days
Whole work: \(\displaystyle5+1\frac{2}{3}=6\frac{2}{3}\) days