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If pipe A can fill the cistern with capacity of the cistern? B fill the cistern It/min. Together, they are able to fill the cliten in 15 minutes, What is the

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(A) 60 liters

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(B) 240 liters

(C) 100 liters

(D) 600 liters

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It looks like you posted a partial question from a test or quiz, likely involving pipes filling a cistern. I will try to reconstruct and solve the problem based on the information provided.

### Problem Interpretation

1. **Pipe A** can fill a cistern in 20 minutes.
2. **Pipe B** can fill the cistern in \( x \) minutes.
3. Together, **Pipe A** and **Pipe B** can fill the cistern in 15 minutes.
4. We need to find the total capacity of the cistern (the answer choices suggest it's in liters).

Let's solve for the unknowns step by step.

### Solution Steps

#### Step 1: Determine the Rate of Each Pipe

- The rate of Pipe A filling the cistern is \(\frac{1}{20}\) cisterns per minute because it fills the cistern in 20 minutes.
- The rate of Pipe B filling the cistern is \(\frac{1}{x}\) cisterns per minute because it fills the cistern in \( x \) minutes.

#### Step 2: Combine the Rates of Both Pipes

When both pipes are open, their combined rate is:

\[
\frac{1}{20} + \frac{1}{x} = \frac{1}{15}
\]

#### Step 3: Solve for \( x \)

Combine the fractions on the left side:

\[
\frac{x + 20}{20x} = \frac{1}{15}
\]

Cross-multiply to solve for \( x \):

\[
15(x + 20) = 20x
\]

Distribute and simplify:

\[
15x + 300 = 20x
\]

\[
300 = 5x
\]

\[
x = 60
\]

So, Pipe B takes 60 minutes to fill the cistern by itself.

#### Step 4: Find the Capacity of the Cistern

Now, let's determine the capacity of the cistern. We know the combined rate fills the cistern in 15 minutes. The amount of water each pipe would contribute in these 15 minutes is:

\[
\text{Water filled by A} = \left(\frac{1}{20}\right) \times 15 = \frac{15}{20} = 0.75 \, \text{cisterns}
\]

\[
\text{Water filled by B} = \left(\frac{1}{60}\right) \times 15 = \frac{15}{60} = 0.25 \, \text{cisterns}
\]

Together, this sums to 1 cistern (0.75 + 0.25 = 1).

To find the cistern's capacity in liters, consider the total time taken when both pipes fill it:

\[
\text{Total flow rate} = \frac{1}{15} \, \text{cisterns per minute}
\]

If the capacity of the cistern is \(C\) liters, the flow rate in liters per minute would be:

\[
\frac{C}{15} \, \text{liters per minute}
\]

Given the rates of pipes A and B in liters per minute:

\[
\frac{C}{20} + \frac{C}{60} = \frac{C}{15}
\]

Substitute to simplify:

\[
\frac{60C + 20C}{1200} = \frac{C}{15}
\]

Simplify further:

\[
\frac{80C}{1200} = \frac{C}{15}
\]

Multiplying by 1200:

\[
80C = 1200 \cdot \frac{C}{15}
\]

Solve for \(C\):

\[
80C = 80C \implies C = 240 \text{ liters}
\]

### Conclusion

The total capacity of the cistern is **240 liters**. The correct answer is **(B) 240 liters**.

Would you like more details, or have any questions?

### Follow-up Questions

1. How would the solution change if Pipe A filled the cistern in 30 minutes instead of 20?
2. What if both pipes working together filled the cistern in 10 minutes instead of 15?
3. How do different flow rates impact the time taken to fill the cistern?
4. How would the answer change if Pipe B's flow rate doubled?
5. Can you apply the concept of combined rates to other real-life scenarios?

### Tip

Always break down problems involving rates into smaller steps, dealing first with individual contributions before combining them.

Learn how to solve a problem involving Pipe A and Pipe B filling a cistern together in 15 minutes. Calculate the capacity of the cistern using rates and linear equations. Suitable for students in Grades 7-9.

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