A cell divides every minute. It will fill a 100 ml beaker in one hour. How much time would it take to fill 50 ml beaker

Options

A. 30 minutes
B. 48 minutes
C. 50 minutes
D. 59 minutes

Answer

To solve the problem, we need to understand the process of cell division and how it relates to the volume of the beaker being filled.

### Step-by-Step Solution:

1. **Understanding the Division Rate**:
- The problem states that a cell divides every minute. This means that the number of cells doubles every minute.

2. **Volume Filled in One Hour**:
- It is given that the cells fill a 100 ml beaker in one hour (60 minutes).

3. **Volume Progression**:
- At the start (0 minutes), the volume is 0 ml.
- After 1 minute, the volume is 1 cell (let's assume this is a small volume).
- After 2 minutes, the volume is 2 cells.
- After 3 minutes, the volume is 4 cells.
- This doubling continues until 60 minutes, where it reaches 100 ml.

4. **Finding the Volume at Each Minute**:
- The volume filled at each minute can be represented as:
- 1 minute: 1 ml
- 2 minutes: 2 ml
- 3 minutes: 4 ml
- 4 minutes: 8 ml
- 5 minutes: 16 ml
- 6 minutes: 32 ml
- 7 minutes: 64 ml
- 8 minutes: 128 ml (which exceeds 100 ml)
- Therefore, at 59 minutes, the volume would be half of 100 ml, which is 50 ml.

5. **Conclusion**:
- Since the beaker reaches 100 ml at 60 minutes, it must have been at 50 ml just one minute before that, at 59 minutes.
- Therefore, it will take **59 minutes to fill a 50 ml beaker**.

### Final Answer:
It will take **59 minutes** to fill a 50 ml beaker.