There are two taps A and B to fill up a water tank. The tank can be filled in 48 min, if both taps are on. The same tank can be filled in 60 min, if tap A alone is on. How much time will tap B alone take, to fill up the same tank?

Options

A. 240 min
B. 180 min
C. 296 min
D. 220 min

Answer

To solve the problem, we need to determine how long it will take for tap B alone to fill the tank. We will use the information provided about the filling times of taps A and B.

### Step-by-Step Solution:

1. **Determine the filling rates of taps A and B:**
- Tap A can fill the tank in 60 minutes. Therefore, the rate of tap A (efficiency) is:
\[ \text{Efficiency of A} = \frac{1 \text{ tank}}{60 \text{ minutes}} = \frac{1}{60} \text{ tanks per minute} \]

2. **Determine the combined filling rate of taps A and B:**
- When both taps A and B are on, they can fill the tank in 48 minutes. Thus, the combined rate of taps A and B is:
\[ \text{Efficiency of A + B} = \frac{1 \text{ tank}}{48 \text{ minutes}} = \frac{1}{48} \text{ tanks per minute} \]

3. **Set up the equation for the efficiency of tap B:**
- Let the efficiency of tap B be \( x \). According to the rates we have:
\[ \text{Efficiency of A} + \text{Efficiency of B} = \text{Efficiency of A + B} \]
\[ \frac{1}{60} + x = \frac{1}{48} \]

4. **Solve for \( x \):**
- Rearranging the equation gives:
\[ x = \frac{1}{48} - \frac{1}{60} \]
- To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 48 and 60 is 240.
- Convert the fractions:
\[ \frac{1}{48} = \frac{5}{240}, \quad \frac{1}{60} = \frac{4}{240} \]
- Now, substituting back:
\[ x = \frac{5}{240} - \frac{4}{240} = \frac{1}{240} \]

5. **Determine the time taken by tap B to fill the tank:**
- Since the efficiency of tap B is \( \frac{1}{240} \) tanks per minute, the time taken by tap B to fill the tank is the reciprocal of its efficiency:
\[ \text{Time taken by B} = \frac{1 \text{ tank}}{\frac{1}{240} \text{ tanks per minute}} = 240 \text{ minutes} \]

### Final Answer:
Tap B alone will take **240 minutes** to fill the tank.