On Thursday, the company’s shares rose in price by a certain amount of percent, and on Friday they fell in price

On Thursday, the company’s shares rose in price by a certain amount of percent, and on Friday they fell in price by the same amount of percent. As a result, they began to cost 36% less than at the opening of trading on Thursday. How much did the company’s shares rise in price on Thursday?

1. Let’s designate the initial price of shares for x.

We will take 100% as a unit.

2. On Thursday, shares went up by a certain number of percent, even if by y.

This means that on Thursday the shares began to cost x * (1 + y).

3. On Friday, they fell by (1 – y) percent.

It turns out: x * (1 + y) * (1 – y)

4. Shares became 36% cheaper, that is, they cost 64% of the original price.

It turns out equality: x (1 + y) (1 – y) = 0.64x

5. Reduce both sides of the equation by x and solve the equation.

(1 + y) (1 – y) = 0.64

1 ^ 2 – y ^ 2 = 0.64

– y ^ 2 = 0.64 – 1

-y ^ 2 = – 0.36

y ^ 2 = 0.36

y = 0.6

6. Let’s translate into percent – it turns out 60%.

Answer: 60%