Question

A and B can do a work in 8 days; B and C in 12 days; A, B and C together in 6 days. In how many days will A and C together do it?

• A. 9
• B. 6
• C. 8
• D. 10
• E. 12

Hint:

To find the combined rate of two individuals, subtract the known pair rates from the triple rate to isolate individual speeds, then add them back together.

Answer 1

The Correct Option is C

Step 1: Analyse options.
- Work rate of $(A+B+C) = 1/6$. - Work rate of $(A+B) = 1/8$. - Work rate of $C = (A+B+C) - (A+B) = 1/6 - 1/8 = 1/24$. - Work rate of $(B+C) = 1/12$. - Work rate of $A = (A+B+C) - (B+C) = 1/6 - 1/12 = 1/12$. - Work rate of $(A+C) = 1/12 + 1/24 = 3/24 = 1/8$.
Step 2: Conclusion.
A and C together will complete the work in 8 days. Final Answer: (c) 8