Question : A and B can do a piece of work in 8 days, B and C can do the same work in 12 days and A, B, and C complete it in 6 days. Find the number of days required to finish the work by A and C is:
Option 1: 16
Option 2: 8
Option 3: 12
Option 4: 24
Correct Answer: 8
Solution :
Let the total work is 1 unit.
The efficiency of A and B is $\frac{1}{8}$, the efficiency of B and C is $\frac{1}{12}$ and the efficiency of A, B, and C is $\frac{1}{6}$.
Efficiency of A = Efficiency of (A, B, C) – Efficiency of (B, C)
$= \frac{1}{6} – \frac{1}{12} = \frac{1}{12}$
Efficiency of C = Efficiency of (A, B, C) – Efficiency of (A, B)
$= \frac{1}{6} – \frac{1}{8} = \frac{1}{24}$
Efficiency of (A + C) = Efficiency of A + Efficiency of C
$= \frac{1}{12} + \frac{1}{24} = \frac{3}{24} = \frac{1}{8}$
Hence, the number of days required to finish the work by A and C is 8 days.
Hence, the correct answer is 8.
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