Question

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
be take?
h
(2) 4
(1) 3
(3) 7
(4) 5​

Answer 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

be take?

h

(2) 4

(1) 3

(3) 7

(4) 5

​ Explanatory Answer

Method of solving this CAT Question from Races: Understanding of relative speed would help.

Let track length be equal to T.

Time taken to meet for the first time = Trelativespeed = T6−b or Tb−6

Time taken for a lap for A = T6

Time taken for a lap for B = Tb

So, time taken to meet for the first time at the starting point = LCM (T6,Tb) = THCF(6,b)

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 6−bHCF(6,b) = 2 or b−6HCF(6,b) = 2

The question is " If two people 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?"

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

Hence, the answer is 3.

Choice A is the correct answer.