Two pipes can fill a tank in 20 minutes and 30 minutes respectively. If both the pipes are opened simultaneously, then the tank will be filled in

Options

A. 10 minutes
B. 12 minutes
C. 15 minutes
D. 25 minutes

Answer

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

### Step-by-Step Solution:

1. **Determine the rate of the first pipe:**
The first pipe can fill the tank in 20 minutes. Therefore, in 1 minute, it fills:
\[ \text{Rate of first pipe} = \frac{1}{20} \text{ of the tank per minute} \]

2. **Determine the rate of the second pipe:**
The second pipe can fill the tank in 30 minutes. Therefore, in 1 minute, it fills:
\[ \text{Rate of second pipe} = \frac{1}{30} \text{ of the tank per minute} \]

3. **Combine the rates of both pipes:**
When both pipes are opened simultaneously, the total rate of filling the tank is the sum of the individual rates:
\[ \text{Combined rate} = \frac{1}{20} + \frac{1}{30} \]

4. **Find a common denominator:**
The least common multiple (LCM) of 20 and 30 is 60. We can rewrite the rates with a common denominator:
\[ \frac{1}{20} = \frac{3}{60} \quad \text{and} \quad \frac{1}{30} = \frac{2}{60} \]
Therefore:
\[ \text{Combined rate} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} \]

5. **Simplify the combined rate:**
\[ \frac{5}{60} = \frac{1}{12} \]
This means that together, both pipes fill \(\frac{1}{12}\) of the tank in 1 minute.

6. **Calculate the time to fill the tank:**
If both pipes together fill \(\frac{1}{12}\) of the tank in 1 minute, then the time taken to fill the entire tank is:
\[ \text{Time} = 12 \text{ minutes} \]

### Final Answer:
The tank will be filled in **12 minutes** when both pipes are opened simultaneously.

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