A tank can be filled by a tap in 20 min and by another tap in 60 min. Both the taps are kept open for 5 min and then the 1st tap is shut off. After this, how much time the tank will be completely filled?

Options

A. 20 min
B. 30 min
C. 45min
D. 40 min

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the filling rates of both taps.
- **Tap 1** fills the tank in 20 minutes. Therefore, its filling rate is:
\[ \text{Rate of Tap 1} = \frac{1 \text{ tank}}{20 \text{ min}} = \frac{3 \text{ units}}{1 \text{ min}} \quad (\text{assuming tank capacity is 60 units}) \]

- **Tap 2** fills the tank in 60 minutes. Therefore, its filling rate is:
\[ \text{Rate of Tap 2} = \frac{1 \text{ tank}}{60 \text{ min}} = \frac{1 \text{ unit}}{1 \text{ min}} \]

### Step 2: Calculate the combined filling rate when both taps are open.
- When both taps are open, the combined filling rate is:
\[ \text{Combined Rate} = \text{Rate of Tap 1} + \text{Rate of Tap 2} = 3 \text{ units/min} + 1 \text{ unit/min} = 4 \text{ units/min} \]

### Step 3: Calculate the amount of water filled in the first 5 minutes.
- In 5 minutes, the amount of water filled by both taps is:
\[ \text{Water filled in 5 min} = \text{Combined Rate} \times 5 \text{ min} = 4 \text{ units/min} \times 5 \text{ min} = 20 \text{ units} \]

### Step 4: Determine the remaining capacity of the tank.
- Since the total capacity of the tank is 60 units, the remaining capacity after 5 minutes is:
\[ \text{Remaining Capacity} = 60 \text{ units} - 20 \text{ units} = 40 \text{ units} \]

### Step 5: Calculate the time taken by Tap 2 to fill the remaining capacity.
- After 5 minutes, Tap 1 is shut off, and only Tap 2 is left to fill the remaining 40 units. Since Tap 2 fills at a rate of 1 unit per minute, the time taken to fill the remaining capacity is:
\[ \text{Time taken by Tap 2} = \frac{\text{Remaining Capacity}}{\text{Rate of Tap 2}} = \frac{40 \text{ units}}{1 \text{ unit/min}} = 40 \text{ minutes} \]

### Final Answer:
- Therefore, the total time taken to fill the tank completely after both taps are opened for 5 minutes and then Tap 1 is shut off is:
\[ \text{Total Time} = 5 \text{ minutes} + 40 \text{ minutes} = 45 \text{ minutes} \]