Two taps can fill a tank in 12 min and 18 min respectively. Both the taps are kept open for 2 min and then the tap that fills the tank in 12 min is turned off. In how many more minutes will the tank be filled?

Options

A. 9
B. 12
C. 13
D. 10

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the filling rates of each tap.
- **Tap A** fills the tank in 12 minutes. Therefore, in 1 minute, it fills:
\[ \text{Rate of Tap A} = \frac{1}{12} \text{ tank/min} \]
- **Tap B** fills the tank in 18 minutes. Therefore, in 1 minute, it fills:
\[ \text{Rate of Tap B} = \frac{1}{18} \text{ tank/min} \]

### Step 2: Find the combined filling rate of both taps.
- When both taps are open, their combined rate is:
\[ \text{Combined Rate} = \text{Rate of Tap A} + \text{Rate of Tap B} = \frac{1}{12} + \frac{1}{18} \]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 12 and 18 is 36. Thus:
\[ \frac{1}{12} = \frac{3}{36}, \quad \frac{1}{18} = \frac{2}{36} \]
- Therefore:
\[ \text{Combined Rate} = \frac{3}{36} + \frac{2}{36} = \frac{5}{36} \text{ tank/min} \]

### Step 3: Calculate the amount of tank filled in the first 2 minutes.
- In 2 minutes, the amount of tank filled by both taps is:
\[ \text{Amount filled in 2 minutes} = 2 \times \frac{5}{36} = \frac{10}{36} = \frac{5}{18} \text{ of the tank} \]

### Step 4: Determine the remaining part of the tank to be filled.
- The total capacity of the tank is 1 (the whole tank). Thus, the remaining part of the tank is:
\[ \text{Remaining part} = 1 - \frac{5}{18} = \frac{18}{18} - \frac{5}{18} = \frac{13}{18} \]

### Step 5: Calculate the time taken by Tap B to fill the remaining part.
- After 2 minutes, Tap A is turned off, and only Tap B is left filling the tank. The rate of Tap B is:
\[ \text{Rate of Tap B} = \frac{1}{18} \text{ tank/min} \]
- Let \( x \) be the time in minutes that Tap B takes to fill the remaining \( \frac{13}{18} \) of the tank:
\[ \frac{1}{18} \times x = \frac{13}{18} \]
- Solving for \( x \):
\[ x = 13 \text{ minutes} \]

### Final Answer:
The tank will be filled in **13 more minutes** after Tap A is turned off.

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