The traffic lights at three different road crossings change after every 50 seconds, 75 seconds and 100 seconds respectively. If they all change simultaneously at 9:15 a.m., then find the time (in a.m.) at which they will change simultaneously again?
Show answer & explanation
Correct answer: C
Explanation
Given:
Time intervals = 50 seconds, 75 seconds, 100 seconds
Start time = 9:15 AM
Time when they change together again = LCM (50, 75, 100)
50 = 2 × 5²
75 = 3 × 5²
100 = 2² × 5²
LCM = 2² × 3 × 5² = 4 × 3 × 25 = 300 seconds
300 seconds = 5 minutes
Therefore, the new time = 9:15 + 5 minutes = 9:20