Question

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

• A. 20
• B. 30
• C. 40
• D. 60

Hint:

Sum pairwise work rates and subtract to find individual rates in work problems.

Answer 1

The Correct Option is B

We need to find A’s time to complete the task alone.
- Step 1: Define rates: A’s rate = \( a \), B’s = \( b \), C’s = \( c \).
- Step 2: Equations:
- \( a + b = \frac{1}{12} \)
- \( b + c = \frac{1}{15} \)
- \( a + c = \frac{1}{20} \)
- Step 3: Add equations:
\[ 2(a + b + c) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5 + 4 + 3}{60} = \frac{1}{5} \] \[ a + b + c = \frac{1}{10} \] - Step 4: Find \( a \):
\[ a = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30} \] Time = \( \frac{1}{\frac{1}{30}} = 30 \) days.
- Step 5: Options:
- (b) 30: Correct.
Thus, the answer is b.