Question

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

• A. 20
• B. 30
• C. 40
• D. 45

Answer 1

The Correct Option is A

To solve the problem, we need to determine the rate at which the outlet pipe empties the tank.

First, let's define the rates:

• Rate of the inlet pipe filling the tank = $\frac{1}{8}$ tank per hour.
• Effective rate with both pipes open = $\frac{1}{10}$ tank per hour.

The rate at which the outlet pipe empties the tank can be calculated as:

$\frac{1}{8}-\frac{1}{10}=\frac{1}{40}$ tank per hour.

This means the outlet pipe alone will empty $\frac{1}{40}$ of the tank in one hour.

We need to find how long it takes for the outlet pipe to make a full tank become half-full. This is essentially half the tank capacity:

$\left(\frac{1}{2}\right)÷\frac{1}{40}=20$ hours.

Thus, the outlet pipe alone can make the full tank half-full in 20 hours.