2. 2.1. Dealer Dima bought a "LADA Kalina" car from the manufacturer and increased its price by $A \%$. There was no demand, and Dima had to sell the car at a sale with a $20 \%$ discount. As a result, his profit was $20 \%$. Find $A$.
Answer: 50.

## Solution.

1st method. Let's assume Dima bought a car from the manufacturer for $X$ rubles. After raising the price, the car cost $X(1+A / 100)$ rubles. After reducing the price by $20 \%$, the car cost $0.8 X(1+A / 100)$. According to the condition, this is the same as $1.2 X$. Therefore, $1+A / 100=1.2 / 0.8$, which means $A=50$.

2nd method. After increasing by A\%, the price increased by ( $1+A / 100$ ) times. After reducing the price by $20 \%$, the price is multiplied by 0.8 and becomes 1.2 times the purchase price. Then, $(1+A / 100) \cdot 0.8=1.2$. Therefore, $1+A / 100=1.2: 0.8=1.5$, from which $=50$.