Question
Download Solution PDFSeven bells ring at intervals of 2, 3, 4, 6, 8, 9 and 12 minutes, respectively. They started ringing simultaneously at 7.10 in the morning. What will be the next time when they all ring simultaneously?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Seven bells ring at intervals of 2, 3, 4, 6, 8, 9, and 12 minutes, respectively.
They started ringing simultaneously at 7:10 a.m.
Formula Used:
The time when all bells ring simultaneously is given by the Least Common Multiple (LCM) of their intervals.
Calculation:
Find the LCM of the intervals: 2, 3, 4, 6, 8, 9, and 12.
Prime factorization:
2 = 2
3 = 3
4 = 22
6 = 2 × 3
8 = 23
9 = 32
12 = 22 × 3
LCM = 23 × 32 = 8 × 9 = 72 minutes
Total time = 7:10 a.m. + 72 minutes
72 minutes = 1 hour 12 minutes
⇒ Next simultaneous ringing time = 7:10 a.m. + 1 hour 12 minutes
⇒ 8:22 a.m.
The next time when all the bells ring simultaneously is 8:22 a.m.
Last updated on Jul 16, 2025
-> More than 60.65 lakh valid applications have been received for RPF Recruitment 2024 across both Sub-Inspector and Constable posts.
-> Out of these, around 15.35 lakh applications are for CEN RPF 01/2024 (SI) and nearly 45.30 lakh for CEN RPF 02/2024 (Constable).
-> The Examination was held from 2nd March to 18th March 2025. Check the RPF Exam Analysis Live Updates Here.