Question

How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 10% on the marked price, he earns a profit of 8%.

Answer 1

Hint: First we will take the value of the cost price as some variable and then we have given that the discount is 10% , so we will take y as an increased percentage in the cost value and then perform the given instruction in the question.

Complete step-by-step answer:
Let x = the price of goods.
Let y = percent above the cost price.
Now as per the question the marked price is:
$x+\dfrac{yx}{100}$
Now subtracting 10% from it and finding the profit we get,
$x+\dfrac{yx}{100}-\left( x+\dfrac{yx}{100} \right)\dfrac{10}{100}$
This is the price after 10% discount, now finding profit,
$\begin{align}
  & \dfrac{x+\dfrac{yx}{100}-\left( x+\dfrac{yx}{100} \right)\dfrac{10}{100}-x}{x}\times 100=8 \\
 & \dfrac{\dfrac{9}{10}\left( x+\dfrac{yx}{100} \right)-x}{x}\times 100=8 \\
 & \dfrac{9yx}{10}+90x-100x=8x \\
 & yx=20x \\
 & y=20\% \\
\end{align}$
Hence the shopkeeper must increase the price by 20% to earn a profit of 8%.

Note: The students might get confused in the tricky language they have used so we must read the question carefully and try to understand it and then we should proceed to solve this question. We can also solve this question by taking some values of x and then find the percentage asked in the question.