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?

1. A. 4:00 p.m.
2. B. 4:10 p.m.
3. C. 4:20 p.m.
4. D. 4:30 p.m.

Answer: B

Explanation

For each signal, the duration for green and red colors is the same. So, if a signal takes ‘X’ seconds to change from green to red, it also takes ‘X’ seconds to change from red to green. The total cycle time for each signal (from green to green) is 2X seconds.
Signal 1: Green to Red = 25s. Total cycle = 25s (Green) + 25s (Red) = 50 seconds.
Signal 2: Green to Red = 39s. Total cycle = 39s (Green) + 39s (Red) = 78 seconds.
Signal 3: Green to Red = 60s. Total cycle = 60s (Green) + 60s (Red) = 120 seconds.
They all turn green together at 2:00 p.m. To find when they will turn green together next, we need to find the Least Common Multiple (LCM) of their cycle times (50, 78, 120).
Prime factorization:
50 = 2 × 5^2
78 = 2 × 3 × 13
120 = 2^3 × 3 × 5
LCM(50, 78, 120) = 2^3 × 3 × 5^2 × 13 = 8 × 3 × 25 × 13 = 7800 seconds.
Convert 7800 seconds to minutes: 7800 / 60 = 130 minutes.
Convert 130 minutes to hours and minutes: 130 minutes = 2 hours and 10 minutes.
Since they turned green together at 2:00 p.m., they will turn green together next at 2:00 p.m. + 2 hours 10 minutes = 4:10 p.m.