I'm reading one of the Distance vector protocol RIP and come to know maximum hop count it uses is 15 hops but My doubt is why 15 is used as maximum Hop count why not some other number 10,12 or may be 8 ?
This was a design decision when RIP was created: http://tools.ietf.org/html/rfc1058:
and later on why it was 16:
The 15 as maximum has nothing to do with size of the field which holds metric - this is in fact 4 BYTES in size (max value: 2^32-1): http://tools.ietf.org/html/rfc1723
TL;DR: It was thought at a time that 16 is a big enough to signify infinity, which makes 15 biggest possible network diameter (hop count).
Because in computing, binary form is used for storing numbers. In this case the maximum binary number in four positions would be 15 (1111). So they reserved four digits to count the hops. It seemed to be enough at the time they developed RIP.
Further reading about how the binary system works: