Two taps A and B can fill a tank in 10 hours and 40 hours respectively. In how many hours will the tank be filled, if both the taps were opened simultaneously?

Options

A. 5
B. 6
C. 7
D. 8

Explanation

To solve the problem of how long it will take for two taps A and B to fill a tank when opened simultaneously, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the filling rates of taps A and B:**
- Tap A can fill the tank in 10 hours. Therefore, in one hour, it fills:
\[ \text{Rate of A} = \frac{1}{10} \text{ of the tank} \]
- Tap B can fill the tank in 40 hours. Therefore, in one hour, it fills:
\[ \text{Rate of B} = \frac{1}{40} \text{ of the tank} \]

2. **Add the rates of both taps to find the combined filling rate:**
- When both taps are opened together, their combined filling rate per hour is:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} = \frac{1}{10} + \frac{1}{40} \]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 10 and 40 is 40. Thus, we convert \(\frac{1}{10}\) to have a denominator of 40:
\[ \frac{1}{10} = \frac{4}{40} \]
- Now we can add:
\[ \text{Combined Rate} = \frac{4}{40} + \frac{1}{40} = \frac{5}{40} \]

3. **Simplify the combined rate:**
- The combined rate simplifies to:
\[ \frac{5}{40} = \frac{1}{8} \]
- This means that together, taps A and B fill \(\frac{1}{8}\) of the tank in one hour.

4. **Calculate the time taken to fill the entire tank:**
- If they fill \(\frac{1}{8}\) of the tank in one hour, then to fill the entire tank (1 whole tank), the time taken is the reciprocal of the combined rate:
\[ \text{Time} = \frac{1}{\frac{1}{8}} = 8 \text{ hours} \]

### Final Answer:
The tank will be filled in **8 hours** when both taps A and B are opened simultaneously.