The ratio of efficiencies of two filling pipes is 4 : 5. There is a third emptying pipe which efficiency is two third of the average efficiency of first two filling pipes can empty a filled tank in 36 minutes. In how much time both the filling pipes can fill the tank when it is empty?

Options

A. A) 16 min
B. B) 12 min
C. C) 14 min
D. D) 20 min

Answer

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Define the efficiencies of the filling pipes
Let the efficiency of the first filling pipe be \( 4p \) and the efficiency of the second filling pipe be \( 5p \).

### Step 2: Calculate the average efficiency of the filling pipes
The average efficiency of the two filling pipes can be calculated as follows:
\[ \text{Average Efficiency} = \frac{4p + 5p}{2} = \frac{9p}{2} \]

### Step 3: Determine the efficiency of the emptying pipe
The efficiency of the emptying pipe is given as two-thirds of the average efficiency of the filling pipes:
\[ \text{Efficiency of the emptying pipe} = \frac{2}{3} \times \frac{9p}{2} = 3p \]

### Step 4: Calculate the total work done by the emptying pipe
The emptying pipe can empty a filled tank in 36 minutes. Therefore, the total work done (in terms of efficiency) can be calculated as:
\[ \text{Total Work} = \text{Efficiency} \times \text{Time} = 3p \times 36 = 108p \]

### Step 5: Calculate the time taken by both filling pipes to fill the tank
The combined efficiency of both filling pipes is:
\[ \text{Combined Efficiency} = 4p + 5p = 9p \]
Now, we can find the time taken to fill the tank using the formula:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{108p}{9p} \]
Here, \( p \) cancels out:
\[ \text{Time} = \frac{108}{9} = 12 \text{ minutes} \]

### Final Answer
The time taken by both filling pipes to fill the tank when it is empty is **12 minutes**.

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