Question : In a race around a circular cycling track of 75 km, two cyclists are riding at a speed of 30 km/hr and 25 km/hr. After what time (in hours) will they meet at the point from where they started their journey?
Option 1: 16
Option 2: 7
Option 3: 14
Option 4: 15
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Correct Answer: 15
Solution :
We have,
Two cyclists at a speed of 30 km/hr and 25 km/hr.
A circular cycling track = 75 km.
The time taken by the two cyclists to reach the starting point is $\frac{75}{30}$ hrs and $\frac{75}{25}$ hrs respectively.
Time of meeting at starting track for first time = LCM of time taken by individuals to complete one lap
= LCM ($\frac{75}{30}, \frac{75}{25}$)
= LCM (2.5, 3)
= 15 hrs
Hence, the correct answer is 15.
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