Question

The price of a sweater was slashed from Rs. 960 to Rs. 816 by a shopkeeper in the season. Find the rate of discount given by him.

Answer 1

Hint: We will find the amount of discount by using the relation between the marked price and the selling price. After that, we will find the percentage of discount with respect to the market price. We will use the formula for finding the percentage. For finding the discount percentage, the formula will be given as $ \text{discount }\!\!\%\!\!\text{ }=\dfrac{\text{discount}}{\text{marked price}}\times 100 $ .

Complete step by step answer:
The price of the sweater was Rs. 960 initially. So, Rs. 960 is the marked price of the sweater. The price was reduced to Rs. 816 by the shopkeeper. The new price is the price at which the sweater will be sold. Hence, the selling price of the sweater is Rs. 816. Therefore, the shopkeeper has given a discount on the price of the sweater. The amount of discount given by the shopkeeper is the difference between the marked price and the selling price. We can write a formula for it in the following manner,
 $ \text{discount}=\text{marked price}-\text{selling price} $
Substituting the values of the marked price and the selling price in the above formula, we get
 $ \begin{align}
  & \text{discount}=960-816 \\
 & \therefore \text{discount}=144\text{ Rs} \\
\end{align} $
Now, we have to find the discount percentage. For this, we will use the formula $ \text{discount }\!\!\%\!\!\text{ }=\dfrac{\text{discount}}{\text{marked price}}\times 100 $
Substituting the discount and marked price values in the above formula, we get
 $ \begin{align}
  & \text{discount }\!\!\%\!\!\text{ }=\dfrac{144}{960}\times 100 \\
 & \Rightarrow \text{discount }\!\!\%\!\!\text{ }=\dfrac{12}{80}\times 100 \\
 & \therefore \text{discount }\!\!\%\!\!\text{ }=15 \\
\end{align} $
Hence, the rate of discount given by the shopkeeper is 15%.

Note:
 It is important to understand the relations between marked price, selling price, discount, and profit. It is useful to know these relations and formulae for such types of questions. The key aspect is calculating the percentage of discount with respect to the marked price. We should do the calculations explicitly so that we can avoid making any errors in the calculations and get the correct answer.