Question

A and B can complete a task in 12 days, B and C in 15 days, and A and C in 20 days. How many days will A alone take to complete the task?

• A. 24 days
• B. 30 days
• C. 36 days
• D. 40 days

Hint:

For work rate problems, sum equations and subtract to isolate individual rates.

Answer 1

The Correct Option is B

- Step 1: Let A, B, C's work rates be $a, b, c$ (work/day). Given: $a + b = \frac{1}{12}$, $b + c = \frac{1}{15}$, $a + c = \frac{1}{20}$.
- Step 2: Add all: $2a + 2b + 2c = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5 + 4 + 3}{60} = \frac{12}{60} = \frac{1}{5}$.
- Step 3: So, $a + b + c = \frac{1}{10}$.
- Step 4: Subtract $a + b = \frac{1}{12}$: $c = \frac{1}{10} - \frac{1}{12} = \frac{6 - 5}{60} = \frac{1}{60}$.
- Step 5: From $a + c = \frac{1}{20}$, $a + \frac{1}{60} = \frac{1}{20} \implies a = \frac{1}{20} - \frac{1}{60} = \frac{3 - 1}{60} = \frac{1}{30}$.
- Step 6: Time for A alone = $\frac{1}{a} = 30$ days. Option (2) matches.