Directions: In the following question, two quantities I and II are given. Compare both the quantities and choose the correct option and give answer accordingly.
Quantity I: Pipe A can fill a reservoir in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
Quantity II: 10

Options

A. Quantity I `gt` Quantity II
B. Quantity I `le` Quantity II
C. Quantity I `lt` Quantity II
D. Quantity I `ge` Quantity II

Answer

To solve the problem, we need to determine how long it will take for the reservoir to be filled when all three pipes (A, B, and C) are open simultaneously.

### Step-by-step solution:

1. **Determine the filling rates of each pipe:**
- Pipe A can fill the reservoir in 5 hours. Therefore, its filling rate is:
\[ \text{Rate of A} = \frac{1}{5} \text{ reservoirs per hour} \]
- Pipe B can fill the reservoir in 10 hours. Therefore, its filling rate is:
\[ \text{Rate of B} = \frac{1}{10} \text{ reservoirs per hour} \]
- Pipe C can fill the reservoir in 30 hours. Therefore, its filling rate is:
\[ \text{Rate of C} = \frac{1}{30} \text{ reservoirs per hour} \]

2. **Calculate the combined filling rate of all three pipes:**
- To find the total filling rate when all pipes are open, we add their individual rates:
\[ \text{Total Rate} = \text{Rate of A} + \text{Rate of B} + \text{Rate of C} \]
\[ \text{Total Rate} = \frac{1}{5} + \frac{1}{10} + \frac{1}{30} \]

3. **Finding a common denominator:**
- The least common multiple (LCM) of 5, 10, and 30 is 30. We convert each rate to have a denominator of 30:
\[ \frac{1}{5} = \frac{6}{30}, \quad \frac{1}{10} = \frac{3}{30}, \quad \frac{1}{30} = \frac{1}{30} \]
- Now, adding these fractions:
\[ \text{Total Rate} = \frac{6}{30} + \frac{3}{30} + \frac{1}{30} = \frac{10}{30} = \frac{1}{3} \text{ reservoirs per hour} \]

4. **Calculate the time to fill the reservoir:**
- If the combined rate is \(\frac{1}{3}\) reservoirs per hour, then the time taken to fill one reservoir is the reciprocal of the rate:
\[ \text{Time} = \frac{1}{\text{Total Rate}} = \frac{1}{\frac{1}{3}} = 3 \text{ hours} \]

5. **Compare Quantity I and Quantity II:**
- Quantity I (time taken to fill the reservoir) = 3 hours
- Quantity II = 10 hours

Since 3 hours is less than 10 hours, we conclude that Quantity I is less than Quantity II.

### Final Answer:
The correct option is that Quantity I is less than Quantity II.