Question

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together then the tank will be filled in:

• A. \(3 \frac{9}{17}\) hour
• B. \(3 \frac{7}{9}\) hour
• C. \(3 \frac{9}{12}\) hour
• D. \(3 \frac{7}{17}\) hour

Hint:

When dealing with multiple pipes with different rates, combine their rates by adding the filling rates and subtracting the emptying rates.

Answer 1

The Correct Option is A

Given: \begin{itemize} \item Pipe A fills the tank in 5 hours. \item Pipe B fills the tank in 6 hours. \item Pipe C empties the tank in 12 hours. \end{itemize} \subsection*{Calculation of Rates} \begin{align*} \text{Rate of Pipe A} &= \frac{1}{5} \text{ tank per hour},
\text{Rate of Pipe B} &= \frac{1}{6} \text{ tank per hour},
\text{Rate of Pipe C} &= -\frac{1}{12} \text{ tank per hour}. \end{align*} Combined Rate \begin{align*} \text{Combined rate} &= \left(\frac{1}{5} + \frac{1}{6} - \frac{1}{12}\right) \text{ tanks per hour}
&= \frac{17}{60} \text{ tanks per hour}. \end{align*} Time to Fill the Tank \begin{align*} \text{Time to fill the tank} &= \frac{1}{\frac{17}{60}} = \frac{60}{17} \approx 3 \frac{9}{17} \text{ hours}. \end{align*} Thus, with all pipes open, the tank will be filled in \(3 \frac{9}{17}\) hours, matching option (a).