Simultaneous traffic signals (LCM)
Question
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?
Options
4:00 p.m.
4:10 p.m.
4:20 p.m.
4:30 p.m.
Explanation
The text states that the times given (25, 39, 60 seconds) are for changing from green to red. Because the durations for green and red are identical , a full complete cycle (green + red) for each light takes exactly double that duration:
To find when they simultaneously return to green, compute the Least Common Multiple (LCM) of the full cycles: LCM(50, 78, 120) Prime factorizations: 50 = 2 × 5² 78 = 2 × 3 × 13 120 = 2³ × 3 × 5
LCM = 2³ × 3 × 5² × 13 = 8 × 3 × 25 × 13 = 600 × 13 = 7800 seconds.
Convert 7800 seconds to minutes: 7800 \div 60 = 130 minutes = 2 hours and 10 minutes. Adding this to 2:00 p.m. yields exactly 4:10 p.m[cite: 3873, 3876].
Answer: (b).
Question details
Year
2023
Paper
CSAT
Question
Q50
Section
Numerical Ability
Sub-topic
LCM & HCF
Type
Number theory
Difficulty
Medium
Source hint
Number theory
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