Two pipes A & B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously. How much time will be taken to fill the tank?

Answer

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

### Step-by-Step Solution:

1. **Determine the Total Work**:
We can consider the total work required to fill the tank as 180 units (this is a common multiple of the time taken by both pipes).

2. **Calculate the Efficiency of Pipe A**:
- Pipe A can fill the tank in 36 hours.
- Efficiency of A (EA) = Total Work / Time taken by A = 180 units / 36 hours = 5 units per hour.

3. **Calculate the Efficiency of Pipe B**:
- Pipe B can fill the tank in 45 hours.
- Efficiency of B (EB) = Total Work / Time taken by B = 180 units / 45 hours = 4 units per hour.

4. **Combine the Efficiencies**:
- When both pipes are opened simultaneously, their efficiencies add up.
- Combined Efficiency (E_total) = EA + EB = 5 units/hour + 4 units/hour = 9 units/hour.

5. **Calculate the Time Taken to Fill the Tank**:
- Time taken to fill the tank = Total Work / Combined Efficiency = 180 units / 9 units/hour = 20 hours.

### Final Answer:
The time taken to fill the tank when both pipes A and B are opened simultaneously is **20 hours**.

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