We know that number of coprimes less than a number can be found using Euler's totient function. But if there are two numbers $p$ and $q$ and we need to find number of numbers less than $q$ and coprime to $p$, is there any efficient method?
No. This is as hard as factoring, and there is no known efficient algorithm for factoring. In particular, there is a standard reduction to show that if you could compute Euler's totient function efficiently, then you could factor efficiently.