CAT 2017

Slot 2

QA

Question & Solution

1. Concept Used

• Topic: Time and Work — Pipes and Cisterns
• Formula: $$\text{Net Rate} = \text{Inlet Rate} - \text{Outlet Rate} = \frac{1}{\text{Time taken when both pipes are open}}$$

2. Calculation

Let the time taken by the outlet pipe alone to empty the full tank be $x$ hours.

The inlet pipe alone fills the tank in 8 hours, so its rate of filling = $\frac{1}{8}$ tank per hour.

When both pipes are open, the tank fills in 10 hours, so the net rate = $\frac{1}{10}$ tank per hour.

Using the net rate formula:

$$\frac{1}{8} - \frac{1}{x} = \frac{1}{10}$$

$$\frac{1}{x} = \frac{1}{8} - \frac{1}{10} = \frac{5 - 4}{40} = \frac{1}{40}$$

$$x = 40 \text{ hours}$$

So, the outlet pipe alone empties the full tank in 40 hours.

Now, the question asks: if only the outlet pipe is open, how long does it take for the full tank to become half-full?

This means the outlet pipe needs to drain exactly half the tank.

Since the outlet pipe drains the full tank in 40 hours, it drains half the tank in:

$$\text{Time} = \frac{40}{2} = 20 \text{ hours}$$

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3. Solution

Answer = Option A ✅

The final calculated value is 20 hours. The outlet pipe, which empties the full tank in 40 hours, will take exactly 20 hours to drain half the tank.