Ram, Shyam and Tarun started cycling from a point on a...

Ram, Shyam and Tarun started cycling from a point on a circular track $600 \mathrm{~m}$ long with speeds of $10 \mathrm{~m} / \mathrm{sec}$, $15 \mathrm{~m} / \mathrm{sec}$ and $20 \mathrm{~m} / \mathrm{sec}$ respectively. Find the time taken by them to meet at the starting point for the first time (in seconds). (A) 120 (B) 60 (C) 240 (D) 600

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Key Concepts

Circular Motion

Circular motion involves moving along a back-to-start path, where the motion repeats after completing one full circle. This concept is fundamental when dealing with problems on circular tracks, as it defines the periodic nature of the motion.

Lap Time Calculation

Lap time is the period it takes for an object to complete one full circuit on a circular track. It is calculated by dividing the total length of the track by the object's speed. Understanding lap time is essential for determining synchronization points on the track.

Least Common Multiple (LCM)

The least common multiple is the smallest number that is a multiple of two or more numbers. In the context of cyclic events such as lap times on a circular track, finding the LCM of the individual lap times helps determine when all participants simultaneously return to the starting point.

Synchronization of Periodic Events

Synchronization of periodic events involves aligning events that occur repeatedly with different periods. This is achieved by calculating the LCM of the individual time intervals, which gives the common time point where all events coincide. This concept is widely applicable in solving problems involving cycles.

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