An inlet pipe can fill a tank in 5 hours and an outlet pipe can empty the same tank in 36 hours, working individually. How many additional number of outlet pipes of the same capacity are required to be opened, so that the tank never over flows?

Options

A. 3
B. 6
C. 8
D. 7

Answer

To solve the problem, we need to determine how many additional outlet pipes are required to ensure that the tank does not overflow when the inlet pipe is filling it.

### Step-by-Step Solution:

1. **Determine the filling rate of the inlet pipe:**
- The inlet pipe can fill the tank in 5 hours.
- Therefore, in 1 hour, the inlet pipe fills:
\[ \text{Filling rate of inlet pipe} = \frac{1 \text{ tank}}{5 \text{ hours}} = \frac{1}{5} \text{ tanks/hour} \]
- If we consider the total capacity of the tank as 180 units, then in 1 hour, the inlet pipe fills:
\[ \text{Units filled in 1 hour} = \frac{180 \text{ units}}{5 \text{ hours}} = 36 \text{ units/hour} \]

2. **Determine the emptying rate of the outlet pipe:**
- The outlet pipe can empty the tank in 36 hours.
- Therefore, in 1 hour, the outlet pipe empties:
\[ \text{Emptying rate of outlet pipe} = \frac{1 \text{ tank}}{36 \text{ hours}} = \frac{1}{36} \text{ tanks/hour} \]
- In terms of units, the outlet pipe empties:
\[ \text{Units emptied in 1 hour} = \frac{180 \text{ units}}{36 \text{ hours}} = 5 \text{ units/hour} \]

3. **Set up the equation for the condition of no overflow:**
- For the tank to never overflow, the total outflow must be greater than or equal to the inflow. Let \( x \) be the number of additional outlet pipes required.
- The total emptying rate with \( x \) additional outlet pipes is:
\[ \text{Total emptying rate} = 5 \text{ units/hour} + 5x \text{ units/hour} \]
- The condition for no overflow can be expressed as:
\[ 5 + 5x \geq 36 \]

4. **Solve for \( x \):**
- Rearranging the inequality:
\[ 5x \geq 36 - 5 \]
\[ 5x \geq 31 \]
\[ x \geq \frac{31}{5} \]
\[ x \geq 6.2 \]
- Since \( x \) must be a whole number, we round up to the nearest whole number:
\[ x = 7 \]

5. **Conclusion:**
- Therefore, **7 additional outlet pipes** are required to ensure that the tank never overflows.