We can also solve it like this :
We know nth term of AP tn = Sn - Sn-1 ( where Sn means sum of n terms)
So if sum of p terms = p2 (say)
sum of (p-1) terms = (p-1)2
Hence , pth term can be written as : p2 - (p-1)2 = 2p - 1
Similarly qth term can be written as : q2 - (q-1)2 = 2q -1
Hence the ratio of pth and qth term : (2p-1) / (2q-1)
Hence the correct option is A)