find the original prices of the two houses

Question

The ratio of the prices of two houses was 16:23. Two years later, when the price of the first had risen by 10% and that of the second by 477, the ratio of their prices become 11:20.

Answer 1

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.