A tank is connected with four pipes A, B, C and D of which two are filling the tank and other two are emptying it. The time taken by A, B, C and D to finish their jobs are 10 hours, 15 hours, 20 hours and 30 hours respectively. All four pipes are opened. When the tank was empty, it took 12 hours to fill it completely. Which two are the outlet pipes?

Options

A. A and B
B. C and D
C. A and C
D. B and D

Answer

To solve the problem, we need to determine which two pipes are emptying the tank (outlet pipes) given the time taken by each pipe to fill or empty the tank.

### Step-by-Step Solution:

1. **Identify the Rates of Each Pipe**:
- Pipe A fills the tank in 10 hours, so its rate is \( \frac{1}{10} \) tanks per hour.
- Pipe B fills the tank in 15 hours, so its rate is \( \frac{1}{15} \) tanks per hour.
- Pipe C fills the tank in 20 hours, so its rate is \( \frac{1}{20} \) tanks per hour.
- Pipe D fills the tank in 30 hours, so its rate is \( \frac{1}{30} \) tanks per hour.

2. **Convert Rates to a Common Denominator**:
- The least common multiple (LCM) of 10, 15, 20, and 30 is 60.
- Therefore, we can express the rates in terms of units per hour:
- Pipe A: \( \frac{60}{10} = 6 \) units per hour
- Pipe B: \( \frac{60}{15} = 4 \) units per hour
- Pipe C: \( \frac{60}{20} = 3 \) units per hour
- Pipe D: \( \frac{60}{30} = 2 \) units per hour

3. **Calculate Total Rate When All Pipes Are Open**:
- If all four pipes are opened, the total rate of filling the tank is:
\[ \text{Total Rate} = \text{Rate of A} + \text{Rate of B} - \text{Rate of C} - \text{Rate of D} \]
- Since A and B are filling pipes and C and D are emptying pipes:
\[ \text{Total Rate} = 6 + 4 - 3 - 2 = 5 \text{ units per hour} \]

4. **Determine the Time to Fill the Tank**:
- The problem states that it takes 12 hours to fill the tank when all pipes are open. Therefore, the total units filled in 12 hours is:
\[ \text{Total Units} = \text{Total Rate} \times \text{Time} = 5 \times 12 = 60 \text{ units} \]

5. **Identify the Outlet Pipes**:
- Since the total filling capacity is 60 units and the total rate of filling is 5 units per hour, we can conclude that the pipes C and D, which have rates of 3 and 2 units per hour respectively, are the outlet pipes.
- Therefore, the outlet pipes are C and D.

### Conclusion:
The two outlet pipes are **C and D**.