Question

A can do a piece of work in 10 days. He works at it for 4 days and then B finished the remaining work in 9 days. How long will they take to complete the work if they do it together?

• A. 5 days
• B. 6 days
• C. 4 days
• D. 16 days

Answer 1

Answer:

B. 6 days

1. A's work: In 4 days, A completes $\frac{4}{10} = \frac{2}{5}$ of the total work.

2. Remaining work: $1 - \frac{2}{5} = \frac{3}{5}$ of the work is left.

3. B's total capacity: B completes this $\frac{3}{5}$ work in 9 days, meaning B can do the whole job alone in $9 \times \frac{5}{3} = \mathbf{15\text{ days}}$.

4. Working together: Combined 1-day work = $\frac{1}{10} + \frac{1}{15} = \frac{3+2}{30} = \frac{5}{30} = \frac{1}{6}$.

5. Final Answer: 6 days