Bacterial cell divides every one minute. It takes 15 minutes a cup to be one-fourth full. How much time will it take to fill the cup ?
(a) 30 minutes
(b) 45 minutes
(c) 60 minutes
(d) 17 minutes

Options

A. 30 minutes
B. 45 minutes
C. 60 minutes
D. 17 minutes

Answer

To solve the problem, we need to analyze the information given about the bacterial cell division and the filling of the cup.

### Step-by-Step Solution:

1. **Understanding the Division of Bacteria**:
- The problem states that a bacterial cell divides every one minute. This means that every minute, the number of bacteria doubles.

2. **Analyzing the Filling of the Cup**:
- We are told that it takes 15 minutes for the cup to be one-fourth full. This means that at the end of 15 minutes, the cup is at 25% capacity.

3. **Determining the Half-Full Time**:
- Since the bacteria double in number every minute, if the cup is one-fourth full at 15 minutes, it will be half full at the next minute (16 minutes). This is because doubling the one-fourth full amount (25%) gives us half (50%).

4. **Finding the Full Cup Time**:
- Continuing from the half-full state, the cup will be completely full at the next minute (17 minutes). This is because doubling the half-full amount (50%) results in a full cup (100%).

5. **Conclusion**:
- Therefore, the cup will be completely full in 17 minutes.

### Final Answer:
The time it will take to fill the cup is **17 minutes**. The correct option is (d) 17 minutes.

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