Question

A pipe can fill an empty tank in 15 hours, but due to a leakage at the bottom, it is filled in 20 hours. If the tank is full, how long will the leakage take to empty it if no other entry or exit point in the tank is open?

• A. 50 hours
• B. 60 hours
• C. 40 hours
• D. 30 hours

Answer 1

Answer:

B. 60 hours

The leakage will take 60 hours to empty the full tank completely.

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1. Find the individual work rates

Let's assume the total capacity of the tank is a convenient number, like the Least Common Multiple (LCM) of 15 and 20, which is 60 units.

• Filling Pipe Rate: If it fills the 60-unit tank in 15 hours, its efficiency is:
  $\frac{60}{15} = 4 \text{ units/hour}$

• Net Rate (Pipe + Leak): Due to the leakage, it takes 20 hours to fill the same 60-unit tank, so the combined efficiency is:
  $\frac{60}{20} = 3 \text{ units/hour}$

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2. Calculate the Leakage Rate

The difference between the standalone filling rate and the net filling rate is caused entirely by the leak:
$\text{Leakage Rate} = \text{Filling Pipe Rate} - \text{Net Rate}$
$\text{Leakage Rate} = 4 - 3 = 1 \text{ unit/hour}$

This means the leak empties 1 unit of water every hour.

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3. Determine the Time to Empty a Full Tank

To empty a completely full tank (60 units) at a rate of 1 unit per hour:
$\text{Time Taken} = \frac{\text{Total Capacity}}{\text{Leakage Rate}} = \frac{60 \text{ units}}{1 \text{ unit/hour}} = 60 \text{ hours}$