Question

Samant brought a microwave oven and paid 10% less price than the original price. He sold it with $30\%$ profit on the price he had paid. What percentage of profit did Samant earn on the original price?

Answer 1

Hint: We start solving the problem by assigning a variable for the original cost price of the microwave oven. We then find the price that Samant bought by subtraction $10\%$ from $100\%$ of the original price of the microwave oven. We then find the selling price of the microwave oven by adding to the price that he has bought the microwave oven. We then find the profit that he gets from the original price and then calculate the profit percentage using $\dfrac{\text{profit}}{\text{original cost price}}\times 100$.

Complete step-by-step solution:
According to the problem, we have given that Samant brought microwave oven with $10\%$ less price than the original price. He then sold it with a $30\%$ profit on the price that he has bought and we need to find the profit that he earned on the original price.
Let us assume the original price of the microwave oven be Rs. A. Samant bought it with 10% less price than Rs. A.
So, the cost incurred for Samant for buying a microwave oven is $90\%$ of Rs. as $10\%$ is reduced as a discount.
We know that $x\%$ of y is defined as the x per 100 parts of y i.e., $x\% of y=\dfrac{x}{100}\times y$.
So, the cost incurred to Samant is $\dfrac{90}{100}\times A=0.9A$.
So, Samant bought a microwave oven at a cost of Rs. 0.9A ---(1).
Now, he sold it with a 30% profit on the price he bought the microwave oven.
So, the selling price will be $\left( 100+30 \right)%$ of 0.9A. Because he needs a 30% higher price in order to get that profit.
So, the selling price of the microwave oven is $130\%$ of 0.9A.
Selling price is $\dfrac{130}{100}\times 0.9A$.
$\Rightarrow 1.3\times 0.9A$.
$\Rightarrow 1.17A$.
So, Samant sold a microwave oven at Rs. 1.17A. Now, we need to find what will be the profit percentage of Rs. 1.17A on the original price Rs. A.
Let us first find the profit. We know that profit is defined as the difference in selling price and cost price.
So, we have profit = $Rs.\left( 1.17A-A \right)$.
$\Rightarrow $Profit = $\left( 1.17-1 \right)A$.
$\Rightarrow $Profit =$0.17A$.
We know that profit percentage is defined as $\dfrac{\text{profit}}{\text{original cost price}}\times 100$.
$\Rightarrow $%Profit = $\dfrac{0.17A}{A}\times 100$.
$\Rightarrow $%Profit = $0.17\times 100$.
$\Rightarrow $%Profit = $17\%$.
We have found the percentage of profit that Samant earns on the original cost price is $17\%$.
$\therefore$ The percentage of profit that Samant earns on the original cost price is $17\%$.

Note: We should not multiply the percentage directly without dividing it with 100. We should always calculate % of profit with respect to cost price not with the selling price as the profit is always checked with the cost price. We need to make sure that the selling price will be greater than the cost price if the profit has occurred. If we are getting a negative profit, then it is to be considered as negative.