Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 seconds respectively. In 30 minutes, how many times do they toll together?

1. A

   15

2. B

   20

3. C

   18

4. D

   16

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

• The problem requires finding when multiple events with different periodic intervals will occur simultaneously. This is a classic application of the Least Common Multiple (LCM).
• The LCM of the intervals (2, 4, 6, 8, 10, 12 seconds) is 120 seconds. This is the time it takes for all bells to toll together again after the first time.
• 120 seconds is equal to 2 minutes. In a 30-minute period, the number of 2-minute intervals is 30 / 2 = 15.
• The question states the bells 'commence tolling together', which implies an initial toll at time 0. Therefore, we must add this first toll to the 15 subsequent tolls, for a total of 15 + 1 = 16.

Why Other Options Were Wrong

• Option A: This is a common error where the initial toll at the start (time 0) is forgotten. It only counts the number of times the bells toll together after the first one within the 30-minute period.
• Option B: This result does not correspond to a logical calculation based on the LCM. It might arise from an arithmetic error, such as incorrectly calculating the LCM or the final division.
• Option C: This result is incorrect and likely stems from a miscalculation of the LCM or an error in the final division. For example, if one incorrectly calculated the LCM to be 100 seconds (1.66 min), the result would be approximately 18, but this is not based on correct math.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of Least Common Multiple (LCM) in time-based problems as background academic context rather than a clinical decision trigger.
• This is a general aptitude question, not a clinical one.
• The underlying logic of calculating coinciding events is relevant in clinical settings, such as scheduling multiple medications or treatments that need to be administered at specific, different intervals.
• What if? If the bells did NOT commence tolling together, and we were asked how many times they would toll together between minute 1 and minute 31, the answer would be 15 (at 2, 4, 6...30 minutes).

How to Approach the Question

• First, identify that the question is asking for a common recurrence of multiple events. This points to using the Least Common Multiple (LCM).
• List the individual time intervals: 2, 4, 6, 8, 10, and 12 seconds.
• Calculate the LCM of these numbers to find the single time interval at which they all toll together. The LCM is 120 seconds.
• Convert the units to be consistent. The total duration is 30 minutes, and the LCM is 120 seconds (2 minutes).
• Divide the total duration by the LCM interval (30 / 2 = 15) to find the number of recurrences.
• Carefully read the prompt for phrases like 'commence together' or 'start together'. This indicates an event at time 0, which must be added to the total count (15 + 1 = 16).

Concept Tested & Keywords

• Concept Tested: Application of Least Common Multiple (LCM) in time-based problems.
• Stem keywords: six bells, commence tolling together, intervals, 2, 4, 6, 8, 10, 12 seconds, 30 minutes
• Lead-in keywords: how many times

Question ID

Qfqo0ASOSpYDCx6RJYOqJ3

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