Let house prices be A and B.
Before the change of price A/B=16/23. So A=16B/23.
Afterwards, 1.1A/(B+477)=11/20.
Substitute for A: 1.1(16B/23)/(B+477)=11/20.
Cross-multiply: 22(16B/23)=11B+5247. Divide through by 11:
32B/23=B+477; cross-multiply again: 32B=23B+10971, so 9B=10971 and B=1219.
Therefore A=16*1219/23=848.
CHECK
A/B=848/1219=16/23. 10% increase of A=932.8.
B goes up to 1696 and the new ratio is 932.8/1696=11/20.