Question

В понедельник акции компании подорожали на некоторое число процентов, а во вторник подешевели на то же самое число процентов. В результате они стали стоить на 4% дешевле, чем при открытии торгов в понедельник. На сколько процентов подорожали акции компании в понедельник?

Answer 1

X - стоимость
P - коэффициент подоражания

$X(1+p)(1-p) = X*0,96$
$1-p^2=0,96$
$p^2=0,04$
$p=0,2$

Изначально подорожали на 20%

Answer 2

Calculating the Percentage Increase in Stock Prices

To calculate the percentage increase in stock prices on Monday, we can use the given information that the stocks became 4% cheaper overall after the changes on Monday and Tuesday.

Let's denote the original price of the stocks as P. After the increase on Monday, the price became P + (P * x/100), where x is the percentage increase. Then, after the decrease on Tuesday, the price became (P + (P * x/100)) - ((P + (P * x/100)) * x/100).

We are given that this final price is 4% cheaper than the original price, so we can set up the equation:

(P + (P * x/100)) - ((P + (P * x/100)) * x/100) = P - (P * 4/100)

Let's solve for x to find the percentage increase in stock prices on Monday.

Calculation

Using the given equation, we can solve for x:

(P + (P * x/100)) - ((P + (P * x/100)) * x/100) = P - (P * 4/100)

Solving for x: (P + (P * x/100)) - (P * x/100 + P * (x^2)/10000) = P - (P * 4/100) P + (P * x/100) - P * x/100 - P * (x^2)/10000 = P - (P * 4/100) P * x/100 - P * (x^2)/10000 = P - (P * 4/100) - P P * x/100 - P * (x^2)/10000 = P - 0.04P - P P * x/100 - P * (x^2)/10000 = -0.04P x/100 - (x^2)/10000 = -0.04 100x - x^2 = -4 x^2 - 100x - 4 = 0

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a) where a = 1, b = -100, and c = -4

Plugging in the values: x = (-(-100) ± √((-100)^2 - 4*1*(-4))) / (2*1) x = (100 ± √(10000 + 16)) / 2 x = (100 ± √10016) / 2 x = (100 ± 100.08) / 2 x = (100 + 100.08) / 2 or x = (100 - 100.08) / 2 x = 200.08 / 2 or x = -0.08 / 2 x = 100.04 or x = -0.04

Since the percentage increase cannot be negative, the percentage increase in stock prices on Monday is 100.04%.

Answer

The stocks of the company increased by 100.04% on Monday.