# 1. CONDITION

According to expert forecasts, apartment prices in Moscow will fall by $20 \%$ in rubles and by $40 \%$ in euros within a year. In Sochi, apartment prices will fall by $10 \%$ in rubles within a year. By how much will apartment prices in Sochi fall in euros? It is assumed that the exchange rate of the euro to the ruble (i.e., the cost of one euro in rubles) is the same in Moscow and Sochi, although it may change over time. Justify your answer.
Solution. Consider equally priced apartments in Moscow and Sochi, let the cost of either be $a$ rubles, which corresponds to $b$ euros. After a year, the cost of the apartment in Moscow will be 0.8 rubles, which is equal to $0.6 b$ euros. From this, $a$ rubles after a year will correspond to $3 b / 4$ euros. In Sochi, the apartment will cost $0.9 a$ rubles. Let's find its price in euros. Since at any given time the exchange rate between rubles and euros is the same for any region, then $0.9 a = 2.7 b / 4 = 0.675 b$. Therefore, the price of the apartment in Sochi will decrease by $0.325 b$ euros, i.e., by $32.5\%$.

Answer: by $32.5\%$.