Question

A shopkeeper marks his goods $20\%$ above the cost price, but allows $10\%$ discount for cash purchase. What percent profit does he make?

Answer 1

Hint: We start solving the problem by assigning the variables for the cost, printed and selling prices. We then find the printed price in terms of cost price using the information that the shopkeeper marks his goods $20\%$ above the cost price. We then find the selling price using the information that the shopkeeper is giving a $10\%$ discount on the printed price. We then substitute the value in $profit\%=\dfrac{selling\ price-\operatorname{cost } price}{\operatorname{cost } price}\times 100$ and make the necessary calculations to get the required result.

Complete step-by-step answer:
According to the problem, A shopkeeper marks his goods $20\%$ above the cost price and allows $10\%$ discount for cash purchase. We need to find the percentage of profit he makes.
Let us assume the cost price, printed price and selling price be c, p and s.
According to the problem, the shopkeeper is printing his 20\% more than the cost price.
So, printed price = $\left( 100+20 \right)\%$ of cost price.
$\Rightarrow $ printed price = $\left( 120 \right)\%$ of cost price.
We know that $x\%$ of y is defined as $\dfrac{x}{100}\times y$.
$\Rightarrow p=\dfrac{120}{100}\times c$.
$\Rightarrow p=1.2c$ ---(1).
Now, the shopkeeper is selling the goods by giving a $10\%$ discount on the printed price.
So, we get the selling price = $\left( 100-10 \right)\%$ of printed price.
$\Rightarrow $ selling price = $90\%$ of printed price.
$\Rightarrow s=\dfrac{90}{100}\times \left( 1.2c \right)$.
$\Rightarrow s=0.9\times \left( 1.2c \right)$.
$\Rightarrow s=1.08c$ ---(2).
Now, let us find the profit percentage on the goods that are sold.
We know that $profit\%=\dfrac{selling\ price-\operatorname{cost } price}{\operatorname{cost } price}\times 100$.
$\Rightarrow profit\%=\dfrac{s-c}{c}\times 100$.
$\Rightarrow profit\%=\dfrac{1.08c-c}{c}\times 100$.
$\Rightarrow profit\%=\dfrac{0.08c}{c}\times 100$.
$\Rightarrow profit\%=0.08\times 100$.
$\Rightarrow profit\%=8\%$.
We have found that the shopkeeper is making $8\%$ profit after selling the goods.
∴ The percentage of profit that the shopkeeper makes after selling the goods is $8\%$.

Note: We can make the mistake by assuming that the shopkeeper is giving a discount on the cost price, which is wrong and ends up in loss. We should always take profit or loss percentage with respect to the cost price, as it is the outflow of money from us. We can also find the profit by subtracting the selling price from the cost price after getting the value of the selling price.