Question

At what percentage above the cost price must an article be marked so as to gain $33\%$ after allowing the customer a discount of $5\%$ ?

Answer 1

Hint: To solve this question we need to know the concept of marked price, cost price and discount. The first step is to make some assumptions and then solve the problem as per the condition given. Formula used to solve the question is $\text{SP = CP + Profit }\!\!\%\!\!\text{ }\!\!\times\!\!\text{ CP}$ and $\text{Marked Price = S}\text{.P - Discount}$ , here $\text{CP}$ and $\text{SP}$are cost price and selling price respectively.

Complete step by step solution:
To find the percentage above the cost price so that a customer gets a discount of $5\%$ and the shopkeeper has a profit of $33\%$ in an article he sells. To start with some assumptions that need to be taken. Let us consider the cost price of an article to be of rupees $100$ and the marked price of the object be rupees $x$. Writing it mathematically we get:
$\text{Cost Price}=100$
$\text{Marked Price}=x$
Since the cost price is $100$ and gain percent is $33\%$so the selling price become:
$\Rightarrow \text{C}\text{.P + 33 }\!\!\%\!\!\text{ }\!\!\times\!\!\text{ C}\text{.P}$
$\Rightarrow 100+33\%\times 100$
$\Rightarrow 100+\dfrac{33}{100}\times 100$
$\Rightarrow 100+33$
$\Rightarrow 133$
So the selling price of the article is rupees $133$.
The second part of the question is that the customer has a discount of $5\%$. On applying this condition we get:
$\Rightarrow x-5\%\times x=133$
$\Rightarrow x-\dfrac{5}{100}\times x=133$
$\Rightarrow \dfrac{95}{100}\times x=133$
$\Rightarrow x=\dfrac{133\times 100}{95}$
$\Rightarrow x=140$
Percentage above the cost price should the article be marked is:
$\Rightarrow \dfrac{\text{Marked price - Cost Price}}{\text{Cost Price}}\times 100$
$\Rightarrow \dfrac{140-100}{100}\times 100$
$\Rightarrow \dfrac{40}{100}\times 100$
$\Rightarrow 40\%$

$\therefore $ At $40\%$ percentage above the cost price must an article be marked so as to gain $33\%$ after allowing the customer a discount of $5\%$.

Note: Marked price is always expressed as the percentage of the cost price. Discount on a material is always applied on the marked price and not on the selling price or cost price. The difference between the marked price and the discount is selling price$\text{Marked price - Discount = Selling Price}$.