At a telephone exchange, three phones ring at intervals of 20sec, 24 sec and 30 seconds. If they ring together at 11:25 a.m, when will they next ring together?
A 11: 29 a.m.
B. 11:27 a.m
C. 11:51 a.m
D 12:29 p.m

Options

A. C
B. A
C. D
D. B

Answer

To solve the problem, we need to find the next time when the three phones will ring together after they initially ring together at 11:25 a.m. The ringing intervals for the phones are 20 seconds, 24 seconds, and 30 seconds. We will find the least common multiple (LCM) of these intervals to determine when they will ring together again.

### Step-by-Step Solution:

1. **Identify the ringing intervals**:
- Phone 1: 20 seconds
- Phone 2: 24 seconds
- Phone 3: 30 seconds

2. **Find the LCM of the intervals**:
- To find the LCM, we can use the prime factorization method:
- 20 = 2^2 × 5
- 24 = 2^3 × 3
- 30 = 2 × 3 × 5

- Now, take the highest power of each prime factor:
- For 2: the highest power is 2^3 (from 24)
- For 3: the highest power is 3^1 (from 24 and 30)
- For 5: the highest power is 5^1 (from 20 and 30)

- Therefore, the LCM is:
\[ LCM = 2^3 × 3^1 × 5^1 = 8 × 3 × 5 = 120 \text{ seconds} \]

3. **Convert LCM to minutes**:
- 120 seconds = 120/60 = 2 minutes

4. **Calculate the next ringing time**:
- The phones ring together at 11:25 a.m. Adding 2 minutes to this time gives:
\[ 11:25 \text{ a.m.} + 2 \text{ minutes} = 11:27 \text{ a.m.} \]

5. **Conclusion**:
- The next time the phones will ring together is at **11:27 a.m.**

### Final Answer:
**B. 11:27 a.m.**