Question : Pipes A, B and C can fill an empty tank in $\frac{30}{7}$ hours if all three pipes are opened simultaneously. A and B are filling pipes and C is an emptying pipe. Pipe A can fill the tank in 15 hours and pipe C can empty it in 12 hours. In how much time (in hours) can pipe B alone fill the empty tank?
Option 1: 3
Option 2: 5
Option 3: 6
Option 4: 4
Correct Answer: 4
Solution :
Let the time taken by B be $x$ hour.
Work done by B in 1 hr = $\frac{1}{x}$
Work done by (A + B – C) in 1 hr = $\frac{7}{30}$
According to the question:
⇒ $\frac{1}{15} + \frac{1}{x} - \frac{1}{12} = \frac{7}{30}$
⇒ $\frac{1}{x} = \frac{7}{30} + \frac{1}{12} - \frac{1}{15}$
⇒ $\frac{1}{x}= \frac{(14 + 5 - 4)}{60}$
⇒ $\frac{1}{x}= \frac{15}{60}$
⇒ $\frac{1}{x}= \frac{1}{4}$
⇒ $x = 4$ hours
Hence, the correct answer is 4.