Answer is (C)
This method helps when log doesn't come to our mind in the exam : )
Here we have options as (B)1/pqr and (D)pqr
so, we try to bring some relation with p,q and r.
Given: p-x = 1/q => 1/px = 1/q
=> (r-z)x = 1/q (Given: r-z = 1/p => p = 1/ r-z => px= (1)x/ (r-z)x )
=> (1/q-y )-xz = 1/q ( Given: q-y = 1/r => r= 1/q -y )
=> 1/(q)xyz = 1/q (we know 1 power anything is "1")
=> xyz =1 (C)