If `5` pipes can fill a tank in `144` minutes , then `6` pipes can fill it in _______ minutes .

Options

A. `120`
B. `130`
C. `110`
D. `90`

Answer

To solve the problem, we need to determine how long it will take for 6 pipes to fill the tank, given that 5 pipes can fill it in 144 minutes. This is an example of inverse proportion, where an increase in the number of pipes leads to a decrease in the time taken to fill the tank.

### Step-by-Step Solution:

1. **Understand the relationship**:
- We know that if 5 pipes can fill the tank in 144 minutes, then the time taken is inversely proportional to the number of pipes. This means that as the number of pipes increases, the time taken decreases.

2. **Set up the equation**:
- Let the number of pipes be \( x \) and the time taken in minutes be \( y \).
- From the problem, we have:
\[ x_1 = 5 \quad \text{and} \quad y_1 = 144 \]
- We need to find \( y_2 \) when \( x_2 = 6 \).

3. **Use the inverse proportion formula**:
- The relationship can be expressed as:
\[ x_1 \cdot y_1 = x_2 \cdot y_2 \]
- Substituting the known values:
\[ 5 \cdot 144 = 6 \cdot y_2 \]

4. **Calculate \( y_2 \)**:
- First, calculate \( 5 \cdot 144 \):
\[ 5 \cdot 144 = 720 \]
- Now, substitute this value back into the equation:
\[ 720 = 6 \cdot y_2 \]
- To find \( y_2 \), divide both sides by 6:
\[ y_2 = \frac{720}{6} = 120 \]

5. **Conclusion**:
- Therefore, 6 pipes can fill the tank in **120 minutes**.