Question

A and B together can complete a work in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A alone complete the work?

• A. 20
• B. 30
• C. 60
• D. 80

Hint:

For work-rate problems, sum pairwise rates and subtract to find individual rates.

Answer 1

The Correct Option is B

Let A, B, C’s work rates be \( a, b, c \) (work/day). 
Given: \( a + b = \frac{1}{12}, b + c = \frac{1}{15}, c + a = \frac{1}{20} \). 
Add all: 
\[ 2(a + b + c) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5 + 4 + 3}{60} = \frac{12}{60} = \frac{1}{5} \] \[ a + b + c = \frac{1}{10} \] \[ a = (a + b + c) - (b + c) = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30} \] Time for A alone = \( \frac{1}{\frac{1}{30}} = 30 \) days. 
Thus, the answer is 30.