If `2//5^(th)` of a cistern is filled in 6 minutes, then what is the time (in minutes) needed to fill the remaining part?

Options

A. 8
B. 9
C. 12
D. 10

Answer

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

### Step 1: Understand the given information
We know that \( \frac{2}{5} \) of the cistern is filled in 6 minutes.

### Step 2: Calculate the time to fill the entire cistern
To find out how long it takes to fill the entire cistern, we can set up a proportion. If \( \frac{2}{5} \) of the cistern takes 6 minutes, then to find the time \( T \) to fill the whole cistern (which is \( 1 \) or \( \frac{5}{5} \)), we can use the formula:

\[ T = \left(\frac{5}{2}\right) \times 6 \]

Calculating this gives:

\[ T = \frac{5 \times 6}{2} = \frac{30}{2} = 15 \text{ minutes} \]

### Step 3: Determine the remaining part to be filled
Since \( \frac{2}{5} \) of the cistern is already filled, the remaining part is:

\[ 1 - \frac{2}{5} = \frac{3}{5} \]

### Step 4: Calculate the time to fill the remaining part
Now we need to find out how long it will take to fill the remaining \( \frac{3}{5} \) of the cistern. Since we know the total time to fill the entire cistern is 15 minutes, and it took 6 minutes to fill \( \frac{2}{5} \), we can find the time to fill the remaining part:

\[ \text{Time to fill remaining part} = \text{Total time} - \text{Time taken to fill } \frac{2}{5} \]

Substituting the values we have:

\[ \text{Time to fill remaining part} = 15 - 6 = 9 \text{ minutes} \]

### Final Answer
Thus, the time needed to fill the remaining part of the cistern is **9 minutes**.

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