Two friends P and Q simultaneously start running from same point around a circular track. They run in the same direction. P runs at 6 m/sec and Q runs at b m/sec. If they cross each other at exactly two points on the circular track and b is a natural number less than 6, then how many values can b take?

Correct option is B

Given

P runs at 6 m/sec and Q runs at b m/sec.

they cross each other at exactly two points on the circular track and b is a natural number less than 6.

Formula used

Time = Distance/relative speed

When running in the same direction, relative speed = a - b.

​Solution:​

Let track length be equal to T.

Time taken to meet for the first time = T/(6 - b)    [b < 6]

Time taken for a lap for A = T/6

Time taken for a lap for B = T/b

The first meeting is planned to take place at the specified starting point. = LCM(T/6,T/b)

= T/HCF(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, basically, we have to find values for b such that = (6 - b)/HCF(6,b) = 2

The only value to satisfy this equation that is less than 6 is 2.

b can take only 1 value.