Question

For a trader, the market price of a refrigerator is Rs. 15,680 inclusive of GST at the rate of 12 % on the market price. Gagan, a customer for this refrigerator, asks the trader to reduce the market price of the refrigerator to such an extent that its reduced price plus GST on it is equal to the market price of the refrigerator. Find the required reduction.

Answer 1

Hint: To solve the given question, we will first assume that the initial market price of the refrigerator is x. Now, we will find the value of x by using the information given in the question that the sum of x and 12 % of GST will be equal to Rs. 15680. After finding the value of x, we will now assume that the reduced marked price of the refrigerator will be y. Now, we will find the value of y by using the information given in the question that the sum of y and 12 % of GST will be equal to x. After finding the value of y, we will find the value of x – y which will be equal to the required reduction in the price of the refrigerator.

Complete step-by-step answer:
To start with, we will assume that the initial market price of the refrigerator is x. Now, it is given in the question that when 12 % of GST is applied to it, the price becomes Rs. 15680. Thus, we can say that the sum of the market price and GST will be equal to Rs. 15680. Thus, we have,
Market Price + GST of 12 % = Rs. 15680
\[\Rightarrow x+12\text{ Percent of x}=Rs.15680\]
\[\Rightarrow x+\dfrac{12}{100}\times x=Rs.15680\]
\[\Rightarrow \dfrac{112x}{100}=Rs.15680\]
\[\Rightarrow x=Rs.15680\times \dfrac{100}{112}\]
\[\Rightarrow x=Rs.14000......\left( i \right)\]
Thus, the initial market price is Rs. 14000.
Now, it is given in the question that the price is reduced to some extent. Let the new price be y. According to the question, the sum of reduced price and GST of 12 % on it is equal to the initial market price of the refrigerator. Thus, we will get the following equation,
Reduced Price + GST of 12 % = Initial Market Price
\[\Rightarrow y+12\text{ Percent of y}=x......\left( ii \right)\]
From (i), we will substitute the value of x in (ii). Thus, we will get,
\[y+\dfrac{12y}{100}=Rs.14000\]
\[\Rightarrow \dfrac{112y}{100}=Rs.14000\]
\[\Rightarrow y=Rs.14000\times \dfrac{100}{112}\]
\[\Rightarrow y=Rs.12500\]
Now, the reduction in the price will be equal to the difference between the reduced price and the initial market price. Thus, we get,
Reduction = Initial Market Price – Reduced Price
\[\Rightarrow \text{Reduction}=x-y\]
\[\Rightarrow \text{Reduction}=Rs.14000-Rs.12500\]
\[\Rightarrow \text{Reduction}=Rs.1500\]

Note: We can also approach the question in the following manner after finding the value of x. Let the reduction in price be z. This reduction in price will make the new price as Rs. 14000 – z. GST on this price will be 12 % of (Rs. 14000 – z). Thus, we can say that,
\[Rs.14000-z+12\text{ Percent of}\left( Rs.14000-z \right)=Rs.14000\]
\[\Rightarrow Rs.14000-z+\dfrac{12}{100}\left( 14000-z \right)=14000\]
\[\Rightarrow -z+\dfrac{12}{100}\times 14000-\dfrac{12}{100}z=0\]
\[\Rightarrow \dfrac{-112z}{100}=-1680\]
\[\Rightarrow z=Rs.1500\]