In Mahabalipuram Temple there are some magical bells which tolls 18 times in a day, simulateneously. But every bell tolls at a different interval of time, but not in fraction of minutes. The maximum number of bells in the temple can be :

Options

A. a.18
B. b.10
C. c.24
D. d.6

Answer

To solve the problem of determining the maximum number of magical bells in the Mahabalipuram Temple that toll 18 times in a day, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Minutes in a Day**:
- There are 24 hours in a day.
- Each hour has 60 minutes.
- Therefore, the total number of minutes in a day is:
\[ 24 \text{ hours} \times 60 \text{ minutes/hour} = 1440 \text{ minutes} \]

2. **Determine the Interval for Each Bell**:
- The bells toll 18 times in a day.
- To find the time interval between each toll, we divide the total minutes by the number of tolls:
\[ \text{Interval} = \frac{1440 \text{ minutes}}{18 \text{ tolls}} = 80 \text{ minutes} \]

3. **Find the Factors of the Interval**:
- We need to find all the factors of 80 since each bell tolls at a different interval of time.
- The prime factorization of 80 is:
\[ 80 = 2^4 \times 5^1 \]
- To find the number of factors, we use the formula for counting factors:
\[ (\text{exponent of } 2 + 1)(\text{exponent of } 5 + 1) = (4 + 1)(1 + 1) = 5 \times 2 = 10 \]
- Therefore, the total number of factors of 80 is 10.

4. **Conclusion**:
- Since each bell tolls at a different interval and there are 10 unique factors of 80, the maximum number of bells that can toll in the temple is:
\[ \text{Maximum number of bells} = 10 \]

### Final Answer:
The maximum number of bells in the temple can be **10**.