Question

A and B can do a 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:

• A. \(7\frac13\) days
• B. \(7\) days
• C. \(7\frac13\) days
• D. \(7\frac13\) days

Answer 1

The Correct Option is A

To solve the problem, first determine the work done per day by A and B:

A takes 10 days to complete the work, so A's work rate is \( \frac{1}{10} \) of the work per day.
B takes 15 days to complete the work, so B's work rate is \( \frac{1}{15} \) of the work per day.

When A and B work together, their combined work rate is:

\(\frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6}\)

This means A and B together can complete \(\frac{1}{6}\) of the work per day.

They work together for 5 days, so the fraction of work completed by them in 5 days is:

\(5 \times \frac{1}{6} = \frac{5}{6}\)

Thus, \(\frac{5}{6}\) of the work is completed. The remaining work is:

\(1 - \frac{5}{6} = \frac{1}{6}\)

A now finishes the remaining \(\frac{1}{6}\) of the work alone. Since A's work rate is \(\frac{1}{10}\) of the work per day, the time A takes to complete the remaining work is:

\(\frac{1/6}{1/10} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3}\) days

Thus, the total time to complete the entire work is:

\(5 + 1\frac{2}{3} = 6\frac{3}{3} + 1\frac{2}{3} = 7\frac{3}{3} = 7\frac{1}{3}\) days

The whole work is completed in \(7\frac{1}{3}\) days.