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Five bells toll together initially and then continue to toll at time intervals of 4, 8, 12, 16 and 20 seconds respectively. If they start tolling simultaneously at 12:00 p.m., then find how many times they will toll together between 12:00 p.m. to 3:00 p.m.
62
54
42
46
46
To find when the bells toll together, calculate the Least Common Multiple (LCM) of 4, 8, 12, 16, and 20. The LCM is 240 seconds, which equals 4 minutes; the bells toll together every 4 minutes. In a 3-hour duration (180 minutes), the bells toll 180 / 4 = 45 times, plus the initial tolling at 12:00 p.m., totaling 46 times.
To find when the bells toll together, calculate the Least Common Multiple (LCM) of 4, 8, 12, 16, and 20. The LCM is 240 seconds, which equals 4 minutes; the bells toll together every 4 minutes. In a 3-hour duration (180 minutes), the bells toll 180 / 4 = 45 times, plus the initial tolling at 12:00 p.m., totaling 46 times.
This problem relies on the mathematical principle of Least Common Multiple (LCM), a fundamental concept used in Time and Work problems often tested in UPSC CSAT and SSC CGL Quantitative Aptitude sections.
LCM of 4, 8, 12, 16, 20 is 240 seconds.
240 seconds corresponds to 4 minutes per interval.
The total count includes the initial toll at 12:00 p.m.
The total time interval is 3 hours (180 minutes).
Formula applied: (Total Time / Interval) + 1.
Option A (62) and B (54) are distractors based on incorrect division or missing the initial start time.
This logic is frequently tested in competitive exams under the 'Number System' and 'Time & Distance' modules.
D is correct тАФ The bells toll together 46 times, including the starting toll, when calculated using the LCM of their intervals over the given 3-hour window.
In competitive exams, always remember to add 1 when calculating events at regular intervals that include the 'starting point' (the 12:00 p.m. toll).
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