Question
Download Solution PDFTwo 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
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.
Calculation
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.
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