Two bells ring at intervals of 59 seconds and 70 seconds. If they both ring at 10 O'clock in the morning together, after how many seconds will they ring together again?

1. A

   4230

2. B

   4030

3. C

   4330

4. D

   4130

Appeared in: RRB Nsg. Superintendent 21 July 2019 (shift 1st)

Explanation

• To find when the two bells will ring together again, we need to calculate the Least Common Multiple (LCM) of their individual ring intervals.
• The intervals are 59 seconds and 70 seconds.
• The number 59 is a prime number, meaning it is only divisible by 1 and itself.
• Since 59 and 70 share no common factors, their LCM is the product of the two numbers.
• Calculation: 59 × 70 = 4130 seconds.

Why Other Options Were Wrong

• Option A: This is an incorrect product of 59 and 70. It may result from a calculation error.
• Option B: This is an incorrect product of 59 and 70. It may result from a calculation error.
• Option C: This is an incorrect product of 59 and 70. It may result from a calculation error.

Related Visual

• Visual 1: Infographic: Explaining the concept of Least Common Multiple (LCM) using a timeline of two bells ringing at different intervals, showing how they eventually align at the LCM.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the Least Common Multiple (LCM) for periodic events as background academic context rather than a clinical decision trigger.
• While this is a math question, the principle of LCM is relevant in clinical scheduling, such as planning medication administration or treatments that must occur at regular, different intervals.
• For example, if one medication is given every 4 hours and another every 6 hours, the LCM (12 hours) tells a nurse when both medications will be due for administration at the same time.
• This skill helps in creating efficient and safe care plans, preventing missed doses or scheduling conflicts.

How to Approach the Question

• Identify the core task: The question asks for the next time two events with different repeating intervals will happen simultaneously.
• Recognize the mathematical concept: This is a classic application of the Least Common Multiple (LCM).
• List the given intervals: Bell 1 rings every 59 seconds, and Bell 2 rings every 70 seconds.
• Analyze the numbers for common factors. Note that 59 is a prime number and does not share any factors with 70.
• Calculate the LCM. Since there are no common factors, their LCM is their product: 59 × 70.
• Perform the multiplication accurately and select the option that matches the result.

Concept Tested & Keywords

• Concept Tested: Calculating the Least Common Multiple (LCM) for periodic events.
• Stem keywords: bells, intervals, 59 seconds, 70 seconds, ring together
• Lead-in keywords: after how many seconds

Question ID

Q9K2d-rCvzqTyfpp2ub7zg

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