Three bells A, B and C toll respectively at intervals of 12 minutes, 24 minutes and 16 minutes. If they toll together at 12:00 am, at what time will they toll together again?
Answers
Final Answer: 12:48 a.m.
Solution:
This is a simple question based on the concept of LCM.
Given that,
- Bell A rings once in every 12 minutes
- Bell B rings once in every 24 minutes
- Bell C rings once in every 16 minutes
Also, they ring together at 12:00 a.m. We are required to find the next time during which, all these bells would ring together.
Let us calculate the LCM of ( 12, 24, 16 ):
Dividing by common divisor 4, we get:
→ ( 3, 6, 4 )
Dividing by common divisor 2, we get:
→ ( 3, 3, 2 )
Dividing by common divisor 3, we get:
→ ( 1, 1, 2 )
Dividing by common divisor 2, we get:
→ ( 1, 1, 1 )
Since ( 1, 1, 1 ) has been obtained, the LCM could be obtained by multiplying all the divisors. Hence we get:
→ 4 × 2 × 3 × 2
→ 48
Hence the LCM of ( 12, 24, 16 ) is 48.
Hence once again after 48 minutes from 12 am, they would ring together.
Hence the time at which all the bells would ring is 12:48 a.m.
Step-by-step explanation:
Given :
- Three bells A, B and C toll respectively at intervals of 12 minutes, 24 minutes and 16 minutes.
- If they toll together at 12:00 am
To Find :
- what time will they toll together again?
Solution :
L.C.M Of ( 12 ,24 , 16 )
12 = 2 x 2 x 3
24 = 2 × 2 × 2 × 3
16 = 2 x 2 × 2 × 2
2 × 2 × 3 × 2 × 2
L.c.m ( 12 ,24 , 16 ) = 2 × 2 × 3 × 2 × 2 = 48 min
According to the Question :
If they toll together at 12:00 am,
12 : 00 + 48
12 : 48 am
Hence 12 : 48 am will they toll together again