The signals at three different road crossings change after every 48 sec, 72 sec and 108 sec. If they change simultaneously at 9:00:00 a.m., at what time will they change simultaneously again?

1. A

   9:07:00 a.m.

2. B

   9:07:12 a.m.

3. C

   9:07:05 a.m.

4. D

   9:07:10 a.m.

Appeared in: DSSSB 12 August 2024

Explanation

• The problem requires finding the smallest time interval that is a multiple of 48, 72, and 108 seconds. This is the definition of the Least Common Multiple (LCM).
• The LCM of 48, 72, and 108 is calculated by finding the prime factors of each number (48=2⁴×3¹, 72=2³×3², 108=2²×3³) and taking the highest power of each prime factor (2⁴×3³).
• The result is 16 × 27 = 432 seconds.
• Converting 432 seconds to minutes and seconds gives 7 minutes and 12 seconds (since 432 = 7 × 60 + 12).
• Adding this duration to the starting time of 9:00:00 a.m. gives the next simultaneous change at 9:07:12 a.m.

Why Other Options Were Wrong

• Option A: This answer corresponds to an interval of exactly 420 seconds (7 minutes). 420 is not divisible by 48, 72, or 108, so it is not a common multiple.
• Option C: This answer corresponds to an interval of 425 seconds (7 minutes and 5 seconds). 425 is not divisible by 48, 72, or 108.
• Option D: This answer corresponds to an interval of 430 seconds (7 minutes and 10 seconds). 430 is not divisible by 48, 72, or 108.

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 synchronization problems as background academic context rather than a clinical decision trigger.
• While this is a mathematical aptitude question, the underlying skill of calculating time intervals is crucial in nursing.
• Nurses use similar calculations for coordinating patient care, such as scheduling multiple medications that need to be administered at different time intervals (e.g., every 4 hours, 6 hours, and 8 hours) to find when they will coincide.
• It is also fundamental for calculating IV drip rates and ensuring treatments are synchronized correctly.

How to Approach the Question

• First, read the question carefully to understand what is being asked. The keywords 'change simultaneously again' indicate a need to find a common point in time for events that repeat at different intervals.
• Recognize that this is a classic Least Common Multiple (LCM) problem. The goal is to find the smallest number that is a multiple of 48, 72, and 108.
• Calculate the LCM of the three numbers. The most reliable method is prime factorization.
• Once the LCM is found in seconds (432), convert this value into minutes and seconds for easier interpretation (7 minutes, 12 seconds).
• Add this calculated time interval to the initial start time (9:00:00 a.m.) to determine the final answer.
• Compare your result with the given options to select the correct one.

Concept Tested & Keywords

• Concept Tested: Application of Least Common Multiple (LCM) in time synchronization problems.
• Stem keywords: signals, road crossings, change simultaneously, 48 sec, 72 sec, 108 sec
• Lead-in keywords: at what time

Question ID

Q5Ox2YehC_PApBJSqCPcxG

Copy ID