# Q. There are three traffic signals. Each signal changes colour from green to red and then from red to green.

The first signal takes 25 seconds, the second signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m, they together turn green. At what time will they change to green next, simultaneously?

(a) 4:00 p.m.

(b) 4:10 p.m.

(c) 4:20 p.m.

(d) 4:30 p.m.

Correct Answer: (b) 4:10 p.m.

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## Synchronization of Traffic Signals

The time taken by each signal to complete a full cycle (green to red and back to green) is twice the time taken to change from green to red. So, the first signal takes 50 seconds, the second signal takes 78 seconds, and the third signal takes 120 seconds to complete a full cycle.

To find out when all three signals will be green simultaneously again, we need to find the least common multiple (LCM) of these three times.

The LCM of 50, 78, and 120 is 7800 seconds.

7800 seconds is equivalent to 2 hours and 10 minutes.

So, if all three signals were green at 2:00 p.m., they will all be green simultaneously again at 4:10 p.m.

Therefore, the correct answer is (b) 4:10 p.m.