A pipe can fill an oil-drum in 40 minutes. Another pipe can empty it in 60 minutes. When 2/3rd part of drum was filled with oil, the emp tying pipe was opened and 15 minutes later, it was closed. Now, in how much time the drum will be filled, if filling pipe is opened?

Options

A. `23(1)/(3)` min.
B. 25 min.
C. 23 min.
D. 30 min.

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Determine the rates of filling and emptying the drum
- The filling pipe can fill the drum in 40 minutes.
- The emptying pipe can empty the drum in 60 minutes.

**Rate of filling pipe (A)**:
\[ \text{Rate of A} = \frac{1 \text{ drum}}{40 \text{ minutes}} = \frac{3}{120} \text{ drums/minute} \]

**Rate of emptying pipe (B)**:
\[ \text{Rate of B} = \frac{1 \text{ drum}}{60 \text{ minutes}} = \frac{2}{120} \text{ drums/minute} \]

### Step 2: Calculate the effective rate when both pipes are open
- When both pipes are open, the effective rate is:
\[ \text{Effective Rate} = \text{Rate of A} - \text{Rate of B} = \frac{3}{120} - \frac{2}{120} = \frac{1}{120} \text{ drums/minute} \]

### Step 3: Calculate the volume of oil in the drum
- The drum is filled to 2/3 of its capacity. Assuming the total volume of the drum is 120 liters (for ease of calculation):
\[ \text{Volume filled} = \frac{2}{3} \times 120 = 80 \text{ liters} \]

### Step 4: Calculate the volume emptied in 15 minutes
- The emptying pipe is opened for 15 minutes. The volume emptied during this time is:
\[ \text{Volume emptied} = \text{Rate of B} \times \text{Time} = \frac{2}{120} \times 15 = 30 \text{ liters} \]

### Step 5: Calculate the remaining volume in the drum
- After the emptying pipe is closed, the remaining volume in the drum is:
\[ \text{Remaining volume} = 80 - 30 = 50 \text{ liters} \]

### Step 6: Calculate the volume still needed to fill the drum
- The total volume of the drum is 120 liters, so the volume still needed to fill the drum is:
\[ \text{Volume needed} = 120 - 50 = 70 \text{ liters} \]

### Step 7: Calculate the time required to fill the remaining volume
- Now, we need to find out how long it will take to fill the remaining 70 liters using the filling pipe:
\[ \text{Time} = \frac{\text{Volume needed}}{\text{Rate of A}} = \frac{70}{\frac{3}{120}} = 70 \times \frac{120}{3} = 2800 \text{ minutes} \]

### Final Answer
The time required to fill the drum after the emptying pipe is closed and the filling pipe is opened is **2800 minutes**.

---