A cistern is provided by two taps A and B. A can fill it in 20 minutes and B in 25 minutes. Both the taps are kept open for 5 minutes and then the second is turned off. The cistern will be complete filled in another

Options

A. 11 min
B. 10 min
C. 15 min
D. 12 min

Answer

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

### Step 1: Determine the total work
The total work done by the cistern can be represented in terms of the least common multiple (LCM) of the times taken by taps A and B to fill the cistern.

- Tap A can fill the cistern in 20 minutes.
- Tap B can fill the cistern in 25 minutes.

The LCM of 20 and 25 is 100. Therefore, we can consider the total work of the cistern as 100 units.

### Step 2: Calculate the efficiency of each tap
Next, we will calculate the efficiency of each tap in terms of units of work done per minute.

- Efficiency of Tap A = Total Work / Time taken by A = 100 / 20 = 5 units per minute.
- Efficiency of Tap B = Total Work / Time taken by B = 100 / 25 = 4 units per minute.

### Step 3: Calculate the combined efficiency
Now, we will find the combined efficiency when both taps A and B are open.

- Combined Efficiency of A and B = Efficiency of A + Efficiency of B = 5 + 4 = 9 units per minute.

### Step 4: Calculate the work done in 5 minutes
Now, we will calculate how much work is done when both taps are open for 5 minutes.

- Work done in 5 minutes = Combined Efficiency × Time = 9 units/minute × 5 minutes = 45 units.

### Step 5: Calculate the remaining work
Now we will find out how much work is left to be done after 5 minutes.

- Remaining work = Total Work - Work done in 5 minutes = 100 - 45 = 55 units.

### Step 6: Calculate the time taken to fill the remaining work with Tap A only
After 5 minutes, Tap B is turned off, and only Tap A continues to fill the cistern.

- Since Tap A's efficiency is 5 units per minute, we can calculate the time required to fill the remaining work.

Time = Remaining Work / Efficiency of A = 55 units / 5 units per minute = 11 minutes.

### Final Answer
The cistern will be completely filled in another **11 minutes** after Tap B is turned off.

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