The traffic lights at three road crossings change after every 40, 60 and 90 seconds respectively. If they all change together at 9:15 a.m., at what time will they next change together?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9:21 a.m.
The lights change together again after the least common multiple of their intervals.
\(40=2^{3}\times5\), \(60=2^{2}\times3\times5\), \(90=2\times3^{2}\times5\)
LCM \(=2^{3}\times3^{2}\times5=360\) seconds
\(360\div60=6\) minutes
9:15 a.m. \(+\) 6 minutes \(=\) 9:21 a.m.
The lights next change together at 9:21 a.m.
Why the other options are incorrect
Option (1) 9:27 a.m. — Incorrect. 12 minutes is a common multiple, but the lights change together earlier, after 6 minutes.
Option (2) 9:24 a.m. — Incorrect. 9 minutes \(=540\) seconds, which is not a multiple of 40.
Option (4) 9:19 a.m. — Incorrect. 4 minutes \(=240\) seconds, which is not a multiple of 90.