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The problem involves both inlet and outlet pipes filling and emptying a pool. Let's break it down step-by-step.

### Given Data:
- Inlet pipes fill the pool in **10 hours**.
- Outlet pipes empty the pool in **20 hours**.
- There are **16 total pipes** (inlet + outlet).
- With all 16 pipes open, the pool is filled in **4 hours**.

### Let:
- \( x \) = number of inlet pipes.
- \( y \) = number of outlet pipes.

### Work Done by Pipes:
- One inlet pipe can fill \( \frac{1}{10} \) of the pool in 1 hour.
- One outlet pipe can empty \( \frac{1}{20} \) of the pool in 1 hour.

Thus, the total work done by the inlet pipes per hour is:
\[
x \times \frac{1}{10} = \frac{x}{10}
\]
The total work done by the outlet pipes per hour is:
\[
y \times \left(-\frac{1}{20}\right) = -\frac{y}{20}
\]
(The outlet pipes do negative work because they empty the pool.)

### Net Work Done with All Pipes Open:
When all pipes are open, the net work done in 1 hour is:
\[
\frac{x}{10} - \frac{y}{20}
\]
We are told that the pool fills up in **4 hours** with all pipes open. Therefore, the net work done per hour is:
\[
\frac{1}{4}
\]

Equating the two expressions for work done:
\[
\frac{x}{10} - \frac{y}{20} = \frac{1}{4}
\]
Multiply through by 20 to eliminate the denominators:
\[
2x - y = 5 \quad \text{(Equation 1)}
\]

### Total Number of Pipes:
We are also told that there are 16 total pipes, i.e.:
\[
x + y = 16 \quad \text{(Equation 2)}
\]

### Solving the System of Equations:
From Equation (2), we have:
\[
y = 16 - x
\]
Substitute this into Equation (1):
\[
2x - (16 - x) = 5
\]
Simplify:
\[
2x - 16 + x = 5
\]
\[
3x = 21
\]
\[
x = 7
\]

Substitute \( x = 7 \) into Equation (2):
\[
7 + y = 16
\]
\[
y = 9
\]

### Conclusion:
The number of outlet pipes is **9**, and the number of inlet pipes is **7**. Therefore, the number of outlet pipes is **2 more** than the number of inlet pipes.

The correct answer is option **3) 2**.

---

Would you like more details or further clarification on any part of the solution?

Here are 5 related questions for further practice:
1. If the number of inlet pipes doubled, how long would it take to fill the pool?
2. What would happen if all pipes had the same capacity for filling and emptying?
3. How would the solution change if the outlet pipes emptied the pool in 15 hours?
4. If the outlet pipes were closed, how long would it take to fill the pool with only the inlet pipes?
5. What happens if the total number of pipes increases but the filling time remains the same?

**Tip:** When working with problems involving pipes and work rates, always calculate the individual contribution of each type of pipe (inlet/outlet) and sum them up carefully.

A swimming pool is fitted with some inlet pipes and some outlet pipes. Each of the inlet pipes alone takes 10 hours to fill the pool, while each of the outlet pipes alone can empty the pool in 20 hours. If all the 16 pipes are kept open, it takes 4 hours to fill the empty pool completely. Number of outlet pipes is how many more than the number of inlet pipes?

Solve a problem involving inlet and outlet pipes, where inlet pipes take 10 hours to fill a pool and outlet pipes take 20 hours to empty it. Learn how to calculate the number of outlet pipes when the pool fills up in 4 hours with all pipes open. Suitable for Grades 8-10.

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