Answer:
B=5, C=3
Explanation:
Adding two 3-digits number you get 4-digit number, then Q=1 (Q cannot be greater than 1, because 4 + B cannot be greater than 20) and B ≥ 5 (if B < 5, then 4 + B cannot give 2-digits sum).
If B > 5, then the sum will end in digit that is greater than 1 ( 6+6=12 or 6+6+1=13, 7+7=14 or 7+7+1=15, 8+8=16 or 8+8+1=17, 9+9=18 or 9+9+1=19). Here note that B cannot equal to 0, because 4 + B must be 2-digits number.
Thus, B = 5, then P=0. If P = 0, then C = 3 and you get
453 + 557 = 1010.