Question

One bell rings at intervals of 40 minutes and another at intervals of 30 minutes. If they ring at 10 am together, when will they ring together again for the next time?

• A. 12.30 am
• B. 11.30 am
• C. 12.00 Noon.
• D. 1.30pm
• E. 2.00 pm

Answer 1

The Correct Option is C

Step 1: Understand the problem.
We are given that one bell rings at intervals of 40 minutes and another bell rings at intervals of 30 minutes. They both ring together at 10:00 AM. We need to find out when they will ring together again for the next time.

Step 2: Find the time interval for them to ring together again.
The bells will ring together again after the least common multiple (LCM) of their intervals (40 minutes and 30 minutes). We need to calculate the LCM of 40 and 30.

Step 3: Find the LCM of 40 and 30.
The prime factorization of the numbers is:
- 40 = \( 2^3 \times 5 \)
- 30 = \( 2 \times 3 \times 5 \)

To find the LCM, we take the highest power of each prime factor:
- The highest power of 2 is \( 2^3 \)
- The highest power of 3 is \( 3^1 \)
- The highest power of 5 is \( 5^1 \)
Therefore, the LCM is:
LCM = \( 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120 \) minutes.

Step 4: Find when they will ring together again.
Since the LCM is 120 minutes, they will ring together again after 120 minutes, or 2 hours.
If they ring together at 10:00 AM, they will ring together again at 12:00 Noon.

Step 5: Conclusion.
The next time the bells will ring together is at 12:00 Noon.

Final Answer:
The correct option is (C): 12 Noon.