UPSC Prelims 2023 · CSAT
Question 50: Basic Numeracy
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 ?
AnswerUPSC’s answer is (b).
Green to red takes 25 s and red to green takes as long, so full cycles are 50 s, 78 s and 120 s. They turn green together again after the LCM. 50 = 2 x 5^2, 78 = 2 x 3 x 13, 120 = 2^3 x 3 x 5. LCM = 2^3 x 3 x 5^2 x 13 = 7800 s = 130 minutes = 2 h 10 min. From 2:00 p.m. that is 4:10 p.m.
Why each option is right or wrong
- (a) Wrong: 120 minutes = 7200 s has no factor of 13, so it is not a multiple of 78.
- (b) Right: 7800 s = 2 h 10 min after 2:00 p.m.
- (c) Wrong: 140 minutes = 8400 s has no factor of 13.
- (d) Wrong: 150 minutes = 9000 s has no factor of 13.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.