Question

A shopkeeper allows 15% discount on the marked price, still he manages to have 7% profit. How much high did he mark his goods above the cost price?

Answer 1

Answer: $25.9\%$

Step-by-step explanation:

Given

Shopkeeper allows 15% discount on the marked price and still manages a profit of 7%

Suppose the marked price is $x$

So, the selling price is $(1-0.15)x=0.85x$

Suppose the cost price is $y$

$\Rightarrow \dfrac{0.85x-y}{y}=7\%\\\\\Rightarrow \dfrac{0.85x}{y}-1=0.07\\\\\Rightarrow \dfrac{0.85x}{y}=1.07\\\\\Rightarrow y=\dfrac{0.85x}{1.07}\\\\\Rightarrow y=0.794x$

So, the percentage the shopkeeper marked his goods above cost price

$\Rightarrow \dfrac{x-y}{y}\times 100\\\\\Rightarrow \dfrac{x-0.794x}{0.794}\times 100\\\\\Rightarrow \dfrac{0.2056}{0.794x}\times 100\\\\\Rightarrow 25.89\%\approx 25.9\%$