The radius of a circular track is . Two cyclists and start together from the same position at the same time and in the same direction with speeds and respectively. After how many minutes will they meet again at the starting point?

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answer is B.

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Detailed Solution

Concept- Compare the two cyclists' relative speeds. They will re-converge once the quicker one completes exactly one extra rotation than the slower one because they are both travelling in the same direction. And if this meeting place serves as the starting point, this time will serve as the resolution.
Consequently, by using the circle's circumference formula, i.e.

, and taking

, we'll get

Thus, the circumference of the track is.

The cyclists' speeds are indicated by

and

.
Thus the ratio of their speeds is:

Ratio of Speed

Therefore, this ratio tells us that the cyclist

will complete three revolutions in and

will complete 4 revolutions
This is also their first encounter, having made exactly one more revolution than the previous one.
Thus, the moment this instant occurred will be our answer.
The following formula determines how long it

takes to complete one revolution:

Time

, where distance is the length of track i.e.

and speed of

.
Putting these values, we'll get:

Time taken by

for one revolution

Hence, the correct answer is option 2) 12m

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