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?

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

Each signal has equal duration for green and red lights. The full cycle period (green $\to$ red $\to$ green) for each signal is twice its single-color duration: Signal 1 takes $25 + 25 = 50$$\text{ s}$, Signal 2 takes $39 + 39 = 78$$\text{ s}$, and Signal 3 takes $60 + 60 = 120$$\text{ s}$. The signals will turn green simultaneously at the LCM of their cycle times: $\text{LCM}(50,78,120)=7,800\text{ seconds}$$\text{LCM}$(50, 78, 120) = 7,800$\text{ seconds}$. Converting to time: $7800 / 60 = 130$$\text{ minutes}$ = 2$\text{ hours and }$ 10$\text{ minutes}$. Adding this to 2:00 p.m. gives 4:10 p.m.