Answer: 13

Using the last digit
  To get a 7, you could use 1 and 7 or 3 and 9

RRR is 111, 333, 777 or 999
639027$\div$111 = 5757
639027$\div$333 = 1919
639027$\div$777 not an integer
639027$\div$999 not an integer

R = 1, P = 5, Q = 7 $\therefore$ P + Q + R = 13
R = 3, P = 1, Q = 9 $\therefore$ P + Q + R = 13


Using the patterns in the digits
"RRR" = 111 $\times$ R and "PQPQ" = 101 $\times$ "PQ"

639027 = 101 $\times$ "PQ" $\times$ 111 $\times$ R
            = 101 $\times$ 111 $\times$ "PQ" $\times$ R
            = 11211 $\times$ "PQ" $\times$ R

639027 $\div$ 11211 = 57 so "PQ" $\times$ R = 57
57 = 19 $\times$ 3 $\Rightarrow$ R = 3, P = 1, Q = 9 $\therefore$ P + Q + R = 13
or 57 = 57 $\times$ 1 $\Rightarrow$ R = 1, P = 5, Q = 7 $\therefore$ P + Q + R = 13