A and B can complete a piece of work in 12 days, B and C in 8 days and C and A in 8 days. If all of them work together, the time taken in completing the work is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in a day. When the three pairs’ one-day work is added, each person is counted twice, so the sum is twice the one-day work of A, B and C together.
\(\displaystyle 2(A+B+C)=\frac{1}{12}+\frac{1}{8}+\frac{1}{8}=\frac{2+3+3}{24}=\frac{1}{3}\)
\(\displaystyle A+B+C=\frac{1}{6}\) of the work in a day
Time taken together \(=6\) days