A pipe can fill a tank in 10 hours. Due to the leak in its bottom, the tank iş filled in 12 hours. If the tank is full, then that leak can empty the tank in how many hours?

Options

A. 30
B. 45
C. 60
D. 42

Answer

To solve the problem step by step, we will first determine the rates of filling and leaking, and then find out how long it takes for the leak to empty the tank.

### Step-by-Step Solution:

1. **Determine the filling rate of the pipe:**
- The pipe can fill the tank in 10 hours.
- Therefore, the filling rate of the pipe (let's call it \( R_p \)) is:
\[ R_p = \frac{1 \text{ tank}}{10 \text{ hours}} = \frac{1}{10} \text{ tanks per hour} \]

2. **Determine the effective filling rate with the leak:**
- Due to the leak, the tank is filled in 12 hours.
- Therefore, the effective filling rate (let's call it \( R_e \)) is:
\[ R_e = \frac{1 \text{ tank}}{12 \text{ hours}} = \frac{1}{12} \text{ tanks per hour} \]

3. **Determine the rate of the leak:**
- The effective filling rate is the rate of the pipe minus the rate of the leak (let's call the leak rate \( R_l \)):
\[ R_e = R_p - R_l \]
- Substituting the known values:
\[ \frac{1}{12} = \frac{1}{10} - R_l \]

4. **Solve for the leak rate \( R_l \):**
- Rearranging the equation gives:
\[ R_l = \frac{1}{10} - \frac{1}{12} \]
- To subtract these fractions, find a common denominator (which is 60):
\[ R_l = \frac{6}{60} - \frac{5}{60} = \frac{1}{60} \text{ tanks per hour} \]

5. **Determine how long it takes for the leak to empty the tank:**
- If the leak empties \( \frac{1}{60} \) tanks per hour, then the time taken to empty 1 tank (let's call it \( T \)) is the reciprocal of the leak rate:
\[ T = \frac{1 \text{ tank}}{R_l} = \frac{1}{\frac{1}{60}} = 60 \text{ hours} \]

### Final Answer:
The leak can empty the tank in **60 hours**.

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