A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If a

Question

A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o'clock in the morning, at what other time will they all ring together?

Accepted Answer

To find when all three bells will ring together again, we need to find the Least Common Multiple (LCM) of their individual ringing intervals.

1.  Identify the intervals: The bells ring every 18 minutes, 24 minutes, and 32 minutes.

2.  Calculate the LCM of 18, 24, and 32:
    *   Prime factorization:
        *   18 = 2 x 3^2
        *   24 = 2^3 x 3
        *   32 = 2^5
    *   LCM = 2^5 x 3^2 = 32 x 9 = 288 minutes.

3.  Convert the LCM from minutes to hours and minutes:
    *   288 minutes / 60 minutes/hour = 4 hours and 48 minutes (since 4 x 60 = 240, and 288 - 240 = 48).

4.  Add this duration to the initial ringing time:
    *   Initial time: 8:00 AM
    *   Add 4 hours 48 minutes: 8:00 + 4:48 = 12:48 PM.

Therefore, all three bells will ring together again at 12:48 hrs.

Analyzing the options:
A) 12:40 hrs - Incorrect.
B) 12:48 hrs - Correct, as it matches our calculation based on the LCM.
C) 12:56 hrs - Incorrect.
D) 13:04 hrs - Incorrect.

The final answer is B.

Answer

12:40 hrs

Answer

12:48 hrs

Answer

12:56 hrs

Answer

13:04 hrs

A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o'clock in the morning, at what other time will they all ring together?

Explanation

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