# A dealer buys an article at Rs x and sells it for R96 ,thus making a profit of x%.find the value of x.

I assume that "R" represents a unit of currency such as the Chinese Renminbi.

98/x = 1 + x/100

Turn that into a quadratic equation and solve for x. Take the positive root.

This a rather unusual problem since x is used as both an amount currency and a percentage. It makes no sense dimensionally.

## To find the value of x, we can set up an equation based on the given information.

Let's assume the cost price (CP) of the article is Rs x and the selling price (SP) is Rs 96. The profit made is the difference between the selling price and the cost price, which is SP - CP.

Profit = SP - CP

Given that the profit is x% of the cost price, we can express it as:

Profit = (x/100) * CP

Equating the two expressions for profit, we have:

(x/100) * CP = SP - CP

Simplifying the equation, we get:

(x/100) * CP + CP = SP

Now, substitute the given values:

(x/100) * x + x = 96

Multiply through by 100 to eliminate the fraction:

x^2 + 100x = 9600

Rearrange the equation to get a quadratic equation in standard form:

x^2 + 100x - 9600 = 0

Now, you can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 1, b = 100, and c = -9600. Plugging these values into the formula, we get:

x = (-(100) ± √((100)^2 - 4(1)(-9600)))/(2(1))

Simplifying further:

x = (-100 ± √(10000 + 38400))/2

x = (-100 ± √48400)/2

x = (-100 ± 220)/2

Now, we have two possible solutions:

x = (-100 + 220)/2 => x = 120/2 => x = 60

x = (-100 - 220)/2 => x = -320/2 => x = -160

Since profit cannot be negative (as it represents a gain or profit), the value of x in this case is 60.

Therefore, the dealer makes a profit of 60%.