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?

Each signal's complete cycle (from turning green, changing to red, and then changing back to green) is twice the given duration from green to red. Signal 1 cycle: 25 seconds (green to red) + 25 seconds (red to green) = 50 seconds. Signal 2 cycle: 39 seconds (green to red) + 39 seconds (red to green) = 78 seconds. Signal 3 cycle: 60 seconds (green to red) + 60 seconds (red to green) = 120 seconds.

To find when they will next turn green simultaneously, we need to find the Lowest Common Multiple (LCM) of their cycle times: 50, 78, and 120 seconds.

LCM(50, 78, 120): Prime factorization: 50 = 2 * 5^2 78 = 2 * 3 * 13 120 = 2^3 * 3 * 5 LCM = 2^3 * 3 * 5^2 * 13 = 8 * 3 * 25 * 13 = 24 * 25 * 13 = 600 * 13 = 7800 seconds.

Convert 7800 seconds to minutes: 7800 seconds / 60 seconds/minute = 130 minutes.

Convert 130 minutes to hours and minutes: 130 minutes = 2 hours and 10 minutes (since 2 * 60 = 120 minutes).

They together turn green at 2:00 p.m. Adding 2 hours and 10 minutes to this time: 2:00 p.m. + 2 hours 10 minutes = 4:10 p.m.

Therefore, they will change to green next, simultaneously, at 4:10 p.m.

Option A (4:00 p.m.), C (4:20 p.m.), and D (4:30 p.m.) are incorrect because they do not correspond to the calculated LCM of the cycle durations.

The final answer is B) 4:10 p.m.