An outlet pipe can empty a cistern in 5h . In what time will the pipe empty `2/5` part of cistern ?

Answer

To solve the problem, we need to determine how long it will take for an outlet pipe to empty \( \frac{2}{5} \) of a cistern, given that it can empty the entire cistern in 5 hours.

### Step-by-step Solution:

1. **Understand the rate of the pipe:**
The outlet pipe can empty the entire cistern in 5 hours. This means that in 1 hour, the pipe can empty:
\[ \text{Rate of emptying} = \frac{1 \text{ cistern}}{5 \text{ hours}} = \frac{1}{5} \text{ cistern per hour} \]

2. **Determine the time to empty \( \frac{2}{5} \) of the cistern:**
We need to find out how long it takes to empty \( \frac{2}{5} \) of the cistern. If the pipe empties \( \frac{1}{5} \) of the cistern in 1 hour, then to find the time to empty \( \frac{2}{5} \), we can set up the equation:
\[ \text{Time} = \text{Amount to be emptied} \div \text{Rate of emptying} \]
Substituting the values:
\[ \text{Time} = \frac{2/5 \text{ cistern}}{1/5 \text{ cistern per hour}} = 2 \text{ hours} \]

3. **Conclusion:**
Therefore, the time taken to empty \( \frac{2}{5} \) part of the cistern is 2 hours.

### Final Answer:
The pipe will empty \( \frac{2}{5} \) part of the cistern in **2 hours**.

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