Question

A and B can do a job in 6 days. A alone takes 10 days. How long does B take?

• A. 12 days
• B. 15 days
• C. 18 days
• D. 20 days

Hint:

Subtract individual rate from combined rate to find the other's rate, then compute time.

Answer 1

The Correct Option is B

- Step 1: Rates. A's rate = $\frac{1}{10}$ task/day. Combined rate = $\frac{1}{6}$. B's rate = $\frac{1}{6} - \frac{1}{10} = \frac{5 - 3}{30} = \frac{2}{30} = \frac{1}{15}$.
- Step 2: Time for B. Time = $\frac{1}{\frac{1}{15}} = 15$ days.
- Step 3: Verify. Combined: $\frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{1}{6}$.
- Step 4: Conclusion. Option (2) 15 days is correct.