Two bells ring at intervals of 51 seconds and 62 seconds. If they both ring at 10 O'clock in the morning together, after how many seconds will they ring together again?

Appeared in: RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

Explanation

The question asks for the first time two events with different periodic intervals will occur simultaneously, which is a direct application of finding the Least Common Multiple (LCM).
The intervals are 51 seconds and 62 seconds.
To find the LCM, we can use prime factorization: 51 = 3 × 17 and 62 = 2 × 31.
Since 51 and 62 share no common prime factors (they are co-prime), their LCM is the product of the two numbers.
Calculation: 51 × 62 = 3162.
Thus, the bells will ring together again after 3162 seconds.

Option A: This is an incorrect calculation. It is not the product of 51 and 62.
Option B: This is an incorrect calculation. It is not the product of 51 and 62.
Option D: This is an incorrect calculation. It is not the product of 51 and 62.

Visual 1: Infographic: Two parallel timelines, one marked at intervals of 51s, 102s, etc., and the other at 62s, 124s, etc. The visual should highlight that the first point of alignment for both timelines is at 3162s, demonstrating the concept of the Least Common Multiple.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Least Common Multiple (LCM) as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude and logical reasoning, skills that are essential for nurses.
While not a direct clinical scenario, the ability to perform accurate calculations is critical in nursing for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data.
What if the intervals were 12 and 18 seconds? The LCM would not be their product because they share common factors (2 and 3). LCM(12, 18) = 36. The answer would be 36 seconds.

How to Approach the Question

First, identify that the question involves two repeating events with different intervals.
Recognize that the phrase 'ring together again' is a cue to find a common multiple of the intervals.
Since the question asks for the next time they ring together, you need to find the Least Common Multiple (LCM).
Determine the prime factors of each interval (51 and 62).
Check if there are any common prime factors. In this case, there are none.
When numbers are co-prime (no common factors), their LCM is simply their product.

Concept Tested & Keywords

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Practise the full RRB Nsg. Superintendent-21 July 2019 (Shift-2nd)

Attempt every question from this paper in a timed mock, then review the full solution for each one.