Question

Three pipes P, Q and R can fill a tank in 6 hours. After working at it together for 2 hours, R is closed and both P and Q can fill the remaining part in 7 hours. The number of hours that will be taken by R alone to fill the tank is

• A. 10
• B. 12
• C. 14
• D. 16

Answer 1

The Correct Option is C

 To find the time taken by pipe R alone to fill the tank, let's solve step-by-step.

1. \(P\), \(Q\), and \(R\) together can fill the tank in 6 hours. Therefore, the part of the tank filled by \(P + Q + R\) in one hour is:

\(\frac{1}{6}\)

1. They work together for 2 hours, filling:

\(2 \times \frac{1}{6} = \frac{1}{3}\)

of the tank. Hence, the remaining part of the tank is:

\(1 - \frac{1}{3} = \frac{2}{3}\)

1. Pipe R is closed after 2 hours, leaving pipes \(P\) and \(Q\) to fill the remaining \(\frac{2}{3}\) of the tank in 7 hours. Hence, the part of the tank filled by \(P + Q\) in one hour is:

\(\frac{\frac{2}{3}}{7} = \frac{2}{21}\)

1. We know the combined rate of \(P + Q + R\) is \(\frac{1}{6}\), and the rate of \(P + Q\) alone is \(\frac{2}{21}\). So, the rate of \(R\) alone is:

\(\frac{1}{6} - \frac{2}{21} = \frac{7 - 4}{42} = \frac{3}{42} = \frac{1}{14}\)

Therefore, pipe R alone can fill the tank in 14 hours.

Thus, the number of hours that will be taken by R alone to fill the tank is 14.