Question : Pipes A and B can fill an empty tank in 6 and 8 hours respectively, while pipe C can empty the full tank in 10 hours. If all three pipes are opened together, then the tank will get filled in:
Option 1: $4 \frac{4}{23}$ hours
Option 2: $6\frac{1}{5}$ hours
Option 3: $5\frac{5}{23}$ hours
Option 4: $7\frac{1}{2}$ hours
Correct Answer: $5\frac{5}{23}$ hours
Solution :
Hourly work done by A = $\frac{1}{6}$
Hourly work done by B = $\frac{1}{8}$
Hourly work done by C = $\frac{1}{10}$
The tank can be filled by A, B, and C
= $\frac{1}{6}+\frac{1}{8}-\frac{1}{10}$
= $\frac{20+15-12}{120}$
= $\frac{23}{120}$
The tank can be filled in $\frac{120}{23}=5\frac{5}{23}$ hours
Hence, the correct answer is $5\frac{5}{23}$ hours.
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