A pipe can fill a tank in x hours and another can empty it in y hours.They can together fill it in `(y lt x)` -----

Options

A. (x-y) hours
B. (y-x) hours
C. (xy)/(x-y) hours
D. (xy)/(y-x) hours

Answer

To solve the problem, we need to determine how long it will take for a pipe that fills a tank in \( x \) hours and another pipe that empties it in \( y \) hours to fill the tank when both pipes are open together.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two pipes:
- Pipe A fills the tank in \( x \) hours.
- Pipe B empties the tank in \( y \) hours.
- We need to find the time taken to fill the tank when both pipes are open.

2. **Calculate the Capacity of the Tank**:
- Let’s assume the capacity of the tank is the least common multiple (LCM) of \( x \) and \( y \).
- The capacity of the tank can be represented as \( C = xy \) (assuming the tank's capacity is \( xy \) units).

3. **Calculate the Filling Rate of Pipe A**:
- Pipe A fills the tank in \( x \) hours, so its filling rate is:
\[ \text{Rate of Pipe A} = \frac{C}{x} = \frac{xy}{x} = y \text{ units/hour} \]

4. **Calculate the Emptying Rate of Pipe B**:
- Pipe B empties the tank in \( y \) hours, so its emptying rate is:
\[ \text{Rate of Pipe B} = \frac{C}{y} = \frac{xy}{y} = x \text{ units/hour} \]

5. **Calculate the Net Rate When Both Pipes are Open**:
- When both pipes are open, the net rate of filling the tank is:
\[ \text{Net Rate} = \text{Rate of Pipe A} - \text{Rate of Pipe B} = y - x \text{ units/hour} \]

6. **Calculate the Time to Fill the Tank**:
- The time taken to fill the tank when both pipes are open can be calculated using the formula:
\[ \text{Time} = \frac{\text{Tank Capacity}}{\text{Net Rate}} = \frac{C}{\text{Net Rate}} = \frac{xy}{y - x} \]

### Final Answer:
The time taken to fill the tank when both pipes are open is:
\[ \frac{xy}{y - x} \text{ hours} \]