The traffic lights at three different crossings turn red after every $30$ sec, $45$ sec and $60$ sec, respecti

Question

The traffic lights at three different crossings turn red after every $30$ sec, $45$ sec and $60$ sec, respectively. If they all turn red simultaneously at $8:30$ a.m., then at what time will they again turn red simultaneously?

Examoogle · Accepted Answer

The correct answer is Option B: 8:33 a.m.. Find the LCM of 30, 45, and 60. The LCM is 180 seconds. Since 180 seconds = 3 minutes, add 3 minutes to 8:30 a.m. to get 8:33 a.m.

Step-by-Step Solution & Concepts:
Shortcut Trick: Find the LCM of 30, 45, and 60. The LCM is 180 seconds. Since 180 seconds = 3 minutes, add 3 minutes to 8:30 a.m. to get 8:33 a.m.

Formula Used: $$LCM(a, b, c) = 	ext{Smallest multiple divisible by } a, b, 	ext{ and } c$$

Given: Traffic lights turn red at intervals of 30 seconds, 45 seconds, and 60 seconds. They all turned red simultaneously at 8:30 a.m.

Steps: Find the LCM of intervals: To find when the lights turn red together, calculate the Least Common Multiple (LCM) of $30$, $45$, and $60$.. Convert seconds to minutes: Convert the total duration into minutes by dividing by $60$.. Calculate the final time: Add the duration to the initial time of $8:30 	ext{ a.m.}$.

Answer: B is correct because the lights turn red simultaneously again after exactly 3 minutes, making the time 8:33 a.m.

Exam Tip: The LCM method is standard for any 'bells ringing together' or 'runners starting together' problems in competitive exams.

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