Question

A and B together can do a piece of work in 20 days; B and C together in 15 days; C and A together in 12 days. How long will they take to finish the work, working together?

• A. 6 days
• B. 8 days
• C. 10 days
• D. 12 days

Hint:

In these "A+B, B+C, C+A" problems, the total rate is always half the sum of the individual pairs.

Answer 1

The Correct Option is C

Step 1: Concept
Work rate is the reciprocal of time taken.

Step 2: Analysis
$(A+B)$ rate = $1/20$. $(B+C)$ rate = $1/15$. $(C+A)$ rate = $1/12$.

Step 3: Reasoning
Adding them: $2(A+B+C) = 1/20 + 1/15 + 1/12$.
LCM of 20, 15, 12 is 60.
$2(A+B+C) = (3+4+5)/60 = 12/60 = 1/5$.
$(A+B+C) = 1/10$.

Step 4: Conclusion
Working together, they take the reciprocal of $1/10$, which is 10 days. Final Answer: (C)