Question

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

Answer 1

Hint: To solve this problem we need to first know that how to find the X% of a quantity Y. X% of the Y would be given as $X\%\,of\,Y\,=\dfrac{X}{100}\times Y$. First we will find the original price of the refrigerator without GST and after that we will equate the reduced price plus 12% of it’s price with the total amount i.e. original price we obtained and from that we will get the new price of the item. Then from that we will get the reduction in the price required.

Complete step-by-step answer:
We are given the marked price as Rs. 15,680, but this includes 12% GST
First we will assume the initial marked price without GST to be Rs. X
Now it is given that the initial marked price plus GST on it is equal to the original marked price of the refrigerator.
To solve this problem, we should know that what is the meaning of percentage,
Y% Percentage is defined as the Y parts per hundred parts of the given quantity.
And Y% of the Z amount is given by = $\dfrac{Y}{100}\times Z$
Now 12% of the initial price X we get as,
$=\dfrac{12}{100}\times X$
According to the given data, we get the equation as,
$X+12\%\,of\,X=15680$
$\begin{align}
  & X+\dfrac{12}{100}X=15680 \\
 & X+\dfrac{3}{25}X=15680 \\
 & 28X=15680\times 25 \\
 & X=14000 \\
\end{align}$

Hence we get the initial marked price as Rs.14000
Now to find the reduction we will assume the reduction to be Rs. Y
So reduced price we get as = 14000 - Y
Now reduced price plus it’s 12% GST is equal to 14,000, hence we get
\[\left( 14000-Y \right)+\dfrac{12}{100}\left( 14000-Y \right)=14000\]
After solving the above equation, we get,
$Y=1500$
Hence we get the required reduction in price as Rs. 1500.

Note: Many students may make mistakes while solving this question, and may let the amount 14000 to be a new amount and directly then calculate the difference between 15680 and 14000 as required reduction which is wrong. So you need to carefully read the question first and then try to solve it.