Question

Цена товара сначала выросла на 20%,а затем снизилась на 15%,после чего товар стал стоить 102 рубля.Какова была первоначальная стоимость товара?

Answer 1

Пусть первоначальная стоимость товара $p$. После увеличения новая цена станет $1.2p$, после снижения – $1 - 0.15=0.85$ от повышенной цены, то есть $0.85\cdot1.2p=1.02p$.

По условию конечная цена равна 102 рубля, поэтому

$1.02p=102\\p=102:1.02=100$

Ответ. Первоначальная стоимость товара равна 100 рублей.

Answer 2

Calculation of the Initial Cost of the Product

To calculate the initial cost of the product, we need to follow the given information. The price of the product initially increased by 20% and then decreased by 15%. After these changes, the product was priced at 102 rubles.

Let's assume the initial cost of the product as x rubles.

1. The price of the product increased by 20%, which can be calculated as: - New price after the increase = x + (20% of x) = x + 0.2x = 1.2x

2. The price of the product then decreased by 15%, which can be calculated as: - New price after the decrease = 1.2x - (15% of 1.2x) = 1.2x - 0.15(1.2x) = 1.2x - 0.18x = 1.02x

According to the given information, the final price of the product is 102 rubles. So, we can set up the equation:

1.02x = 102

To find the value of x, we can divide both sides of the equation by 1.02:

x = 102 / 1.02 = 100

Therefore, the initial cost of the product was 100 rubles.

Please note that the calculation assumes a linear relationship between the percentage changes in price and the final price.