There are 2 inlet pipes and 1 outlet pipe assigned to fill a tank. If inlet pipe 1 and inlet pipe 2 can fill the tank in 5 hrs and 10 hours respectively and outlet pipe can empty the tank in 15 hrs, then what will be time taken by all three pipes together to fill the tank?

Options

A. A)20/7 hours
B. B)30/7 hours
C. C)15/4 hours
D. D)7 hours

Answer

To solve the problem of how long it will take for two inlet pipes and one outlet pipe to fill a tank, we can follow these steps:

### Step 1: Determine the filling capacity of each pipe
- **Inlet Pipe 1 (A)** can fill the tank in 5 hours.
- **Inlet Pipe 2 (B)** can fill the tank in 10 hours.
- **Outlet Pipe (C)** can empty the tank in 15 hours.

### Step 2: Calculate the efficiency of each pipe
- The efficiency of a pipe is calculated as the total capacity of the tank divided by the time taken to fill or empty it. We can assume the capacity of the tank is 30 units (the least common multiple of 5, 10, and 15).

1. **Efficiency of A**:
\[ \text{Efficiency of A} = \frac{30 \text{ units}}{5 \text{ hours}} = 6 \text{ units/hour} \]

2. **Efficiency of B**:
\[ \text{Efficiency of B} = \frac{30 \text{ units}}{10 \text{ hours}} = 3 \text{ units/hour} \]

3. **Efficiency of C** (as it is an outlet pipe, it will be negative):
\[ \text{Efficiency of C} = -\frac{30 \text{ units}}{15 \text{ hours}} = -2 \text{ units/hour} \]

### Step 3: Calculate the combined efficiency of all pipes
Now, we can sum the efficiencies of all three pipes:
\[ \text{Combined Efficiency} = \text{Efficiency of A} + \text{Efficiency of B} + \text{Efficiency of C} \]
\[ \text{Combined Efficiency} = 6 + 3 - 2 = 7 \text{ units/hour} \]

### Step 4: Calculate the time taken to fill the tank
To find the time taken to fill the tank when all three pipes are working together, we use the formula:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Combined Efficiency}} \]
Here, the total work is the capacity of the tank, which is 30 units:
\[ \text{Time} = \frac{30 \text{ units}}{7 \text{ units/hour}} = \frac{30}{7} \text{ hours} \]

### Final Answer
Thus, the time taken by all three pipes together to fill the tank is \(\frac{30}{7}\) hours.

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