A tank can be filled by one tap in 20 min. and by another in 25 min. Both the taps are kept open for 5 min. and then the second is turned off.In how many minutes more is the tank completely filled ?

Options

A. 17 1/2 min.
B. 12 min.
C. 11 min.
D. 6 min.

Answer

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

### Step 1: Determine the filling rates of the taps
- **Tap A** can fill the tank in 20 minutes. Therefore, in 1 minute, it fills:
\[ \text{Rate of A} = \frac{1}{20} \text{ tank/min} \]
- **Tap B** can fill the tank in 25 minutes. Therefore, in 1 minute, it fills:
\[ \text{Rate of B} = \frac{1}{25} \text{ tank/min} \]

### Step 2: Find the least common multiple (LCM) for the tank capacity
- The LCM of 20 and 25 is 100. This means we can consider the tank's capacity as 100 units.

### Step 3: Calculate the filling rate in units per minute
- The amount filled by Tap A in 1 minute:
\[ \text{Amount filled by A in 1 min} = \frac{100}{20} = 5 \text{ units} \]
- The amount filled by Tap B in 1 minute:
\[ \text{Amount filled by B in 1 min} = \frac{100}{25} = 4 \text{ units} \]

### Step 4: Calculate the combined filling rate of both taps
- When both taps are open, the total amount filled in 1 minute is:
\[ \text{Total rate} = 5 + 4 = 9 \text{ units/min} \]

### Step 5: Calculate the amount filled in the first 5 minutes
- In 5 minutes, the total amount filled by both taps is:
\[ \text{Amount filled in 5 min} = 9 \times 5 = 45 \text{ units} \]

### Step 6: Calculate the remaining capacity of the tank
- The remaining capacity after 5 minutes is:
\[ \text{Remaining capacity} = 100 - 45 = 55 \text{ units} \]

### Step 7: Calculate the time taken to fill the remaining capacity with Tap A
- After 5 minutes, Tap B is turned off, and only Tap A is used to fill the remaining 55 units. The time taken by Tap A to fill the remaining capacity is:
\[ \text{Time} = \frac{\text{Remaining capacity}}{\text{Rate of A}} = \frac{55}{5} = 11 \text{ minutes} \]

### Final Answer
- Therefore, the tank will be completely filled in an additional **11 minutes** after the second tap is turned off.

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