If the seven digit number 876p37q is divided by 225, then the value of p and q respectively are :

225 = 9 × 25, where 9 and 25 are co-primes.
So, a number is divisible by 225 if it is divisible by both 9 and 25
Given number is divisible by 25, only if 7q is divisible by 25, i,e, if q = 5
Sum of digits of given number
= (8 + 7 + 6 + p + 3 + 7 + 5)
= 36 + p, which must be divisible by 9
This is possible if p = 0
Hence, p = 0,   q = 5