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?
Answer & explanation
Answer: (b) 4:10 p.m.
Green and red last equally long, so the full cycles are 50 s, 78 s and 120 s. All three turn green together again after LCM(50, 78, 120) = 7800 s = 2 hours 10 minutes, i.e. at 4:10 p.m.
- Each full cycle (green → red → green) is twice the green time: 2 × 25 = 50 s, 2 × 39 = 78 s, 2 × 60 = 120 s.
- 50 = 2 × 5², 78 = 2 × 3 × 13, 120 = 2³ × 3 × 5.
- LCM = 2³ × 3 × 5² × 13 = 7800 s = 130 minutes = 2 h 10 min.
- 2:00 p.m. + 2 h 10 min = 4:10 p.m.
- Check: LCM(25, 39, 60) = 3900 s, but at that moment the third signal has changed 65 times (an odd number), so it is turning red, not green.
Remember · When signals must show the same colour again, take the LCM of full cycles (both phases), not of the single-phase times.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·