Question

A shopkeeper offers his customers a 10% discount and still makes a profit of 26%. What is the actual cost of an article for him marked Rs. 280?
(a) Rs. 175
(b) Rs. 200
(c) Rs. 215
(d) Rs. 225

Answer 1

Hint: Here, we can assume the cost price of the article to be Rs.x. Then, we will try to calculate the value of x using the conditions given in the problem.

Complete step-by-step answer:
Let us assume that the actual cost of the article is = Rs. x.
Discount means reduction in price of a good or service. It refers to an amount or percentage deducted from the normal selling price of something.
In order to calculate the discount we first multiply the rate by the original price. Then, to calculate the sale price, we subtract the discount from the original price.
Profit is defined as a financial gain, especially the difference between the amount earned and the amount spent in buying, operating or producing something.
Profit percentage is given as:
$\text{Profit }\!\!%\!\!\text{ =}\dfrac{\text{total profit}}{\text{cost price}}\times 100$
We have been given here that the marked price of the article is = Rs. 280
On applying a discount of 10%, the selling price of the article will be:
$\begin{align}
  & SP=Rs.\left( 280-\dfrac{10}{100}\times 280 \right) \\
 & \Rightarrow SP=Rs\left( 280-28 \right)=Rs252 \\
\end{align}$
Now, it is given that the shopkeeper had a profit of 26%.
Since, the cost price of the article is Rs. x.
After applying a profit of 26%, its selling price will be:
$\begin{align}
  & SP=x+\dfrac{26}{100}\times x \\
 & \Rightarrow SP=Rs\dfrac{126x}{100} \\
\end{align}$
Therefore, we can write:
 $\begin{align}
  & \dfrac{126x}{100}=252 \\
 & \Rightarrow 126x=25200 \\
 & \Rightarrow x=\dfrac{25200}{126}=200 \\
\end{align}$
So, the actual cost price of the article is = Rs. x = Rs. 200.
Hence, option (b) is the correct answer.
Note: Students should note here that discount is always applied on the marked price of an article and the profit gained is always added to the cost price to get the selling price.