Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. In how much time the tank will be filled by these pipes if they are opened together?

Options

A. 10 min.
B. 15 min.
C. 12 min.
D. 20 min.

Answer

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

### Step 1: Determine the rates of each pipe
- Pipe A can fill the tank in 20 minutes. Therefore, the rate of pipe A is:
\[ \text{Rate of A} = \frac{1 \text{ tank}}{20 \text{ minutes}} = \frac{1}{20} \text{ tanks per minute} \]

- Pipe B can fill the tank in 30 minutes. Therefore, the rate of pipe B is:
\[ \text{Rate of B} = \frac{1 \text{ tank}}{30 \text{ minutes}} = \frac{1}{30} \text{ tanks per minute} \]

### Step 2: Add the rates of both pipes
When both pipes are opened together, their rates add up:
\[ \text{Combined Rate} = \text{Rate of A} + \text{Rate of B} = \frac{1}{20} + \frac{1}{30} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 20 and 30 is 60. We convert the rates:
\[ \frac{1}{20} = \frac{3}{60}, \quad \frac{1}{30} = \frac{2}{60} \]
Now, we can add them:
\[ \text{Combined Rate} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12} \text{ tanks per minute} \]

### Step 3: Calculate the time to fill the tank
To find the time taken to fill the tank when both pipes are opened together, we use the formula:
\[ \text{Time} = \frac{\text{Volume}}{\text{Rate}} \]
Assuming the volume of the tank is 1 tank, we have:
\[ \text{Time} = \frac{1 \text{ tank}}{\frac{1}{12} \text{ tanks per minute}} = 12 \text{ minutes} \]

### Conclusion
Thus, the time taken to fill the tank when both pipes A and B are opened together is **12 minutes**.

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