A tap can fill a tank in 16 minutes and another can empty it in 8 minutes.If the tank is already half full and both the taps are opned together,the tank will be -----

Options

A. Filled in 12 min.
B. Emptied in 12 min.
C. Filled in 8 min.
D. Emptied in 8 min.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the filling and emptying rates of the taps.
- **Tap A** can fill the tank in 16 minutes.
- **Tap B** can empty the tank in 8 minutes.

### Step 2: Calculate the filling rate of Tap A.
- If Tap A fills the tank in 16 minutes, then in 1 minute, it fills \( \frac{1}{16} \) of the tank.

### Step 3: Calculate the emptying rate of Tap B.
- If Tap B empties the tank in 8 minutes, then in 1 minute, it empties \( \frac{1}{8} \) of the tank.

### Step 4: Find the net effect when both taps are opened together.
- The net rate when both taps are opened is:
\[ \text{Net Rate} = \text{Filling Rate of A} - \text{Emptying Rate of B} = \frac{1}{16} - \frac{1}{8} \]
- To perform this subtraction, we need a common denominator, which is 16:
\[ \frac{1}{8} = \frac{2}{16} \]
- Now, substituting back:
\[ \text{Net Rate} = \frac{1}{16} - \frac{2}{16} = -\frac{1}{16} \]
- This means that the tank is being emptied at a rate of \( \frac{1}{16} \) of the tank per minute.

### Step 5: Determine the current state of the tank.
- The tank is already half full, which means it contains \( \frac{1}{2} \) of the tank's capacity.

### Step 6: Calculate the time taken to empty the tank from half full.
- Since the net effect is emptying the tank at a rate of \( \frac{1}{16} \) of the tank per minute, we can find the time taken to empty \( \frac{1}{2} \) of the tank:
\[ \text{Time} = \frac{\text{Amount to be emptied}}{\text{Net Rate}} = \frac{\frac{1}{2}}{-\frac{1}{16}} = \frac{1}{2} \times -16 = -8 \text{ minutes} \]
- The negative sign indicates that the tank will be empty in 8 minutes.

### Final Answer:
The tank will be empty in 8 minutes.

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