Question

Two pipes can fill a cistern in 14 hours and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it?

• A. 110 hours
• B. 112 hours
• C. 102 hours
• D. 119 hours

Hint:

When calculating the effect of a leak, subtract the leak's rate from the combined filling rate to find its negative effect.

Answer 1

The Correct Option is B

Step 1: Calculate the combined filling rate of the pipes without the leak.
\[ \text{Rate of first pipe} = \frac{1}{14}, \quad \text{Rate of second pipe} = \frac{1}{16} \] \[ \text{Combined rate} = \frac{1}{14} + \frac{1}{16} = \frac{30}{224} = \frac{15}{112} \] \[ \text{Time without leak} = \frac{1}{\frac{15}{112}} = 7.47 \text{ hours} \] With the leak, it took \( 7.47 + \frac{32}{60} \approx 8 \text{ hours}\).

Step 2: Calculate the rate of the leak.
\[ \text{Leak's effect} = \frac{1}{8} - \frac{15}{112} = \frac{1}{112} \] \[ \text{Time to empty} = \frac{1}{\frac{1}{112}} = 112 \text{ hours} \]