CAT Practice : Speed Time, Races

Number Theory combined with Circular Races, whowuda thunk?

Speed Time - Races

    Q.1: Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?
    1. 3
    2. 4
    3. 7
    4. 5


  • Correct Answer
    Choice A. 3

Detailed Solution

Let track length be equal to T.
Time taken to meet for the first time = or

Time taken for a lap for A =
Time taken for a lap for B =

So, time taken to meet for the first time at the starting point = LCM

Number of meeting points on the track = Time taken to meet at starting point/Time taken for first meeting = Relative speed / HCF (6,b).

So, in essence we have to find values for b such that = 2 or = 2

b = 2, 10, 18 satisfy this equation. So, there are three different values that b can take.

Correct Answer: 3

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More questions from Speed Time, Races

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"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi