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%.