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. ✓ UPSC's answer
- (c) 4:20 p.m.
- (d) 4:30 p.m.
Why the answer is (b)
• Each signal's full cycle (green to red and back to green) is twice the given green-to-red duration: Signal 1 = 50s, Signal 2 = 78s, Signal 3 = 120s.
• The signals turn green simultaneously again after the Least Common Multiple (LCM) of their cycle durations.
• LCM of 50, 78, and 120 is calculated as follows: 50 = 2×5², 78 = 2×3×13, 120 = 2³×3×5.
• LCM = 2³ × 3 × 5² × 13 = 8 × 3 × 25 × 13 = 7800 seconds.
• 7800 seconds equals 130 minutes, which is 2 hours and 10 minutes.
• Adding 2 hours and 10 minutes to 2:00 p.m. gives 4:10 p.m.
Why the other options are wrong
- (a) 4:00 p.m.
- 4:00 p.m. corresponds to 7200 seconds, which is not a multiple of 7800 seconds.
- (c) 4:20 p.m.
- 4:20 p.m. corresponds to 8400 seconds, which is not a multiple of 7800 seconds.
- (d) 4:30 p.m.
- 4:30 p.m. corresponds to 9000 seconds, which is not a multiple of 7800 seconds.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.