Question

Цена на товар вначале увеличилась на N1%,а затем снизилась на N2%, после чего она стала равной S руб. Определить исходную цену товара.

Answer 1

Ответ:

10000S/((100-N2)(100+N1))

Пошаговое объяснение:

после повышения пусть цена была х рублей, тогда:

х - 100%

S - 100% - N2%

x = 100S/(100-N2) (рублей)

пусть первоначальная цена у рублей, тогда:

у - 100%

x - 100% + N1%

y = 100x/(100 + N1) = 10000S/((100-N2)(100+N1)) (рублей)

Answer 2

Problem Analysis

We are given that the price of a product initially increased by N1% and then decreased by N2%. After these changes, the price of the product became S rubles. We need to determine the initial price of the product.

Solution

Let's assume the initial price of the product is P rubles.

According to the given information, the price of the product increased by N1% and then decreased by N2%. Mathematically, we can represent this as:

Step 1: Price after the increase: P + (N1/100) * P

Step 2: Price after the decrease: (P + (N1/100) * P) - (N2/100) * (P + (N1/100) * P)

We are also given that the final price of the product is S rubles. So, we can set up the equation:

(P + (N1/100) * P) - (N2/100) * (P + (N1/100) * P) = S

Simplifying the equation:

P + (N1/100) * P - (N2/100) * (P + (N1/100) * P) = S

P + (N1/100) * P - (N2/100) * P - (N2/100) * (N1/100) * P = S

P * (1 + (N1/100) - (N2/100) - (N2/100) * (N1/100)) = S

P * (1 + (N1/100) - (N2/100) - (N2 * N1)/(100 * 100)) = S

P * (1 - (N2/100) - (N2 * N1)/(100 * 100) + (N1/100)) = S

P * (1 - (N2/100) - (N2 * N1)/(100 * 100) + (N1/100)) = S

P * (1 - (N2 + N2 * N1)/(100 * 100) + (N1/100)) = S

P * ((100 * 100 - (N2 + N2 * N1))/(100 * 100) + (N1/100)) = S

P = S / ((100 * 100 - (N2 + N2 * N1))/(100 * 100) + (N1/100))

Now we can substitute the given values of N1, N2, and S to calculate the initial price P.

Calculation

Let's assume N1 = 10, N2 = 20, and S = 1000 for the sake of calculation.

Substituting these values into the equation:

P = 1000 / ((100 * 100 - (20 + 20 * 10))/(100 * 100) + (10/100))

P = 1000 / ((100 * 100 - (20 + 200))/(100 * 100) + (10/100))

P = 1000 / ((100 * 100 - 220)/(100 * 100) + 0.1)

P = 1000 / ((10000 - 220)/(10000) + 0.1)

P = 1000 / (9780/10000 + 0.1)

P = 1000 / (0.978 + 0.1)

P = 1000 / 1.078

P ≈ 927.64

Therefore, the initial price of the product is approximately 927.64 rubles.

Answer

The initial price of the product is approximately 927.64 rubles.

Note: The calculation above is based on the assumption of specific values for N1, N2, and S. Please provide the actual values for N1, N2, and S to get the accurate result.