Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is:

Options

A. 50 minutes
B. 12 minutes
C. 25 minutes
D. 15 minutes

Answer

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

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

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

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

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

### Step 3: Calculate the time taken to fill the tank.
If the combined rate of both pipes is \(\frac{1}{12}\) tank per minute, then the time taken to fill the entire tank (1 tank) is the reciprocal of the combined rate:
\[ \text{Time} = \frac{1 \text{ tank}}{\frac{1}{12} \text{ tank per minute}} = 12 \text{ minutes} \]

### Final Answer:
The time taken to fill the tank when both pipes A and B are opened together is **12 minutes**.

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