Question:medium

A trader marks up a Music system x% over the cost price and gives a discount of (x/4)% to get a profit of (x/2)%. What is his profit percentage?

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Write SP two ways — once from markup and discount, once from the stated profit \(x/2\)% — and equate them to solve for x.
Updated On: Jul 20, 2026
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Solution and Explanation

Substitute $y = \dfrac{x}{100}$ to simplify the algebra before solving.

Marked price factor $= (1+y)$, discount factor $= \left(1-\dfrac{y}{4}\right)$ (since discount is $x/4\% = 100y/4\% $, i.e. fraction $y/4$), and profit factor from the given condition is $\left(1+\dfrac{y}{2}\right)$ (since profit is $x/2\%$).

Setting up the equation:
$(1+y)\left(1-\dfrac{y}{4}\right) = 1+\dfrac{y}{2}$

Expanding the left side:
$1 - \dfrac{y}{4} + y - \dfrac{y^2}{4} = 1 + \dfrac{3y}{4} - \dfrac{y^2}{4}$

So the equation becomes:
$1+\dfrac{3y}{4}-\dfrac{y^2}{4} = 1+\dfrac{y}{2}$

$\dfrac{3y}{4}-\dfrac{y}{2} = \dfrac{y^2}{4}$

$\dfrac{y}{4} = \dfrac{y^2}{4}$

Since $y \ne 0$, dividing both sides by $y/4$ gives $y = 1$, so $x = 100y = 100$.

Profit percentage $= \dfrac{x}{2} = \dfrac{100}{2} = 50\%$.

\[\boxed{Profit\% = 50\%}\]
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