If `(3)/(5)`th of a cistern is filled in 1 minute, the time needed to fill the rest is

Options

A. 40 sec
B. 30 sec
C. 36 sec
D. 24 sec

Answer

To solve the problem, we need to determine how long it will take to fill the remaining part of the cistern after 3/5 of it has been filled in one minute.

### Step-by-Step Solution:

1. **Understand the Problem:**
We know that 3/5 of the cistern is filled in 1 minute. This means that in 1 minute, the cistern is filled to 60% of its capacity.

2. **Determine the Remaining Part:**
Since 3/5 of the cistern is filled, the remaining part is:
\[ 1 - \frac{3}{5} = \frac{2}{5} \]
So, 2/5 of the cistern is still empty.

3. **Calculate the Filling Rate:**
If 3/5 of the cistern is filled in 1 minute (which is 60 seconds), we can find the filling rate per second:
\[ \text{Filling rate} = \frac{3/5 \text{ of the cistern}}{60 \text{ seconds}} = \frac{3}{5 \times 60} = \frac{3}{300} = \frac{1}{100} \text{ of the cistern per second} \]

4. **Determine Time to Fill Remaining Part:**
Now, we need to find out how long it will take to fill the remaining 2/5 of the cistern at the rate of 1/100 of the cistern per second:
\[ \text{Time} = \frac{\text{Remaining part}}{\text{Filling rate}} = \frac{2/5}{1/100} \]
To divide fractions, we multiply by the reciprocal:
\[ \text{Time} = \frac{2}{5} \times \frac{100}{1} = \frac{200}{5} = 40 \text{ seconds} \]

### Final Answer:
The time needed to fill the rest of the cistern is **40 seconds**.