A tap can fill a cistern in 8 hours and another can empty it in 16 hours.If boththe taps are opned simultaneously,the time to fill the tank is------

Options

A. 8
B. 16
C. 16
D. 24

Answer

To solve the problem, we need to determine how long it will take to fill a cistern when one tap fills it and another tap empties it simultaneously.

### Step-by-Step Solution:

1. **Identify the rates of the taps**:
- The first tap can fill the cistern in 8 hours.
- The second tap can empty the cistern in 16 hours.

2. **Calculate the filling rate of the first tap**:
- The rate of the first tap (filling) is \( \frac{1}{8} \) of the cistern per hour.

3. **Calculate the emptying rate of the second tap**:
- The rate of the second tap (emptying) is \( \frac{1}{16} \) of the cistern per hour.

4. **Combine the rates**:
- When both taps are open, the effective rate of filling the cistern is:
\[ \text{Effective rate} = \text{Filling rate} - \text{Emptying rate} = \frac{1}{8} - \frac{1}{16} \]

5. **Find a common denominator**:
- The common denominator for 8 and 16 is 16. Therefore:
\[ \frac{1}{8} = \frac{2}{16} \]
- Now substitute back into the equation:
\[ \text{Effective rate} = \frac{2}{16} - \frac{1}{16} = \frac{1}{16} \]

6. **Determine the time to fill the cistern**:
- Since the effective rate of filling the cistern is \( \frac{1}{16} \) of the cistern per hour, it will take:
\[ \text{Time} = \frac{1 \text{ cistern}}{\frac{1}{16} \text{ cistern/hour}} = 16 \text{ hours} \]

### Final Answer:
The time taken to fill the tank when both taps are opened simultaneously is **16 hours**.

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