Question

A and B together can complete a task in 10 days. A alone can finish it in 15 days. In how many days can B alone finish the work?

• A. 20 days
• B. 25 days
• C. 30 days
• D. 40 days

Hint:

To solve such problems, use the work formula \( \text{Work} = \frac{1}{\text{Time}} \) and combine the rates for A and B together.

Answer 1

The Correct Option is B

Let the total work be \(W\). Work done by A in 1 day = \(\frac{1}{15}\) of \(W\). Work done by A and B together in 1 day = \(\frac{1}{10}\) of \(W\). Let the work done by B in 1 day be \(b\). The total work done by A and B together in 1 day is: \[ \frac{1}{15} + b = \frac{1}{10} \] Solving for \(b\): \[ b = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30} \] Therefore, B alone will take 30 days to finish the work. Answer: \(25\)