Question

Avni wants to buy a dress which is marked at a price of $ Rs4050 $ . GST is applicable at $ 12.5\% $ . However, Avni does not want to pay more than $ Rs4050 $ . She requests the shopkeeper to offer her a discount so that she does not have to pay more than $ Rs4050 $ . Find the selling price that the shopkeeper will sell the dress at. Also, find the discount $ \% $ that the shopkeeper gives.

Answer 1

Hint: In order to find the value after the discount, first find the amount of GST offered, calculate the original price at which the dress can be sold using the formula i.e $ {\text{Total price}} = {\text{Original price}} + GST $ , then from the discount formula, get the percentage of discount offered on the dress.
Formula used:
 $ {\text{Total price}} = {\text{Original price}} + GST $
 $ Discount\% = \dfrac{{\left( {{\text{Total price}}} \right) - \left( {{\text{original price}}} \right)}}{{\left( {{\text{Total price}}} \right)}} \times 100\% $

Complete step by step solution:
We are given that the price of the dress is $ Rs4050 $ , including the GST, $ 12.5\% $ on the original price.
Considering the original price to be $ x $ .
Now, the GST on the original price of dress will be: $ 12.5\% \times \left( {{\text{Original price}}} \right) $
We know that $ \% $ means that per $ 100 $ , so $ 12.5\% $ can be written as $ \dfrac{{12.5}}{{100}} $ removing the decimal, it can be written as $ \dfrac{{125}}{{1000}} $ . Since, we can see that $ 1000 $ is divisible by $ 125 $ , so the simplest form of fraction is: $ \dfrac{1}{8} $ .
Therefore, $ 12.5\% = \dfrac{1}{8} $ .
Substituting this value in the GST price, we get:
 $
  GST = 12.5\% \times \left( {{\text{Original price}}} \right) \\
   \Rightarrow GST = \dfrac{1}{8} \times \left( x \right) \\
   \Rightarrow GST = \dfrac{1}{8}\left( x \right) \;
  $
Since, the total price of the dress is $ Rs4050 $ adding GST to the original price, we get:
 $ {\text{Total price}} = {\text{Original price}} + GST $
 $ Rs4050 = x + \dfrac{1}{8}x $
Multiplying $ 8 $ to the numerator and denominator of $ x $ , in order to have the common denominator:
 $
   \Rightarrow Rs4050 = x + \dfrac{1}{8}x \\
   \Rightarrow Rs4050 = \dfrac{8}{8}x + \dfrac{1}{8}x \;
  $
Adding the common terms, we get:
 $
   \Rightarrow Rs4050 = \dfrac{{8 + 1}}{8}x \\
   \Rightarrow Rs4050 = \dfrac{9}{8}x \;
  $
Multiplying $ \dfrac{8}{9} $ on both the sides:
 $
   \Rightarrow Rs4050 \times \dfrac{8}{9} = \dfrac{9}{8}x \times \dfrac{8}{9} \\
   \Rightarrow Rs4050 \times \dfrac{8}{9} = x \;
  $
Which can be written as:
 $ x = Rs4050 \times \dfrac{8}{9} $
Solving the terms, we get:
 $
  x = Rs\dfrac{{4050 \times 8}}{9} \\
   \Rightarrow x = Rs\dfrac{{32400}}{9} \\
   \Rightarrow x = Rs3600 \;
  $
Therefore, the original price of the dress is $ x = Rs3600 $ at which the dress can be sold.
Hence, the selling price is that the shopkeeper will sell the dress at $ Rs3600 $ .
Now, from the discount formula we know that discount $ \% $ is:
 $ Discount\% = \dfrac{{\left( {{\text{Total price}}} \right) - \left( {{\text{original price}}} \right)}}{{\left( {{\text{Total price}}} \right)}} \times 100\% $
Substituting the total price $ Rs4050 $ , original price $ Rs3600 $ on the above formula, we get:
 $ Discount\% = \dfrac{{4050 - 3600}}{{4050}} \times 100\% $
Solving the equation, we get:
 $
  Discount\% = \dfrac{{450}}{{4050}} \times 100\% \\
   \Rightarrow Discount\% = 0.11111 \times 100\% \\
   \Rightarrow Discount\% = 11.111\% \\
  $
Therefore, the discount offered on the dress is $ 11.111\% $ .
Hence, the discount offered on the dress is $ 11.111\% $ and the price after discount is $ Rs3600 $

Note: If we remove the percentage sign and $ 100 $ from the Discount percentage formula, it would result in the amount of discount offered.
GST is nothing but a kind of tax which is applied on the goods original price, for the country's benefit.