Question

Rehana purchased a dress for Rs.$5400$ including $12\% $ GST. Find the price of the dress before GST was added.

Answer 1

Hint:We are given that Rehana purchased a dress for Rs.$5400$ including $12\% $ GST. So let the original price be $x$ . Then we can write $x + 12\% x = 5400$.Hence find $x$ from this equation to get the value of original price.

Complete step-by-step answer:
GST is tax which increases the original price for the benefit of the country. GST is added on the original price of the item.
Here according to the question Rehana purchased a dress for Rs.$5400$ including $12\% $ GST.
Let the initial price of dress purchased by Rehana be $x$.
Now we know $12\% $ GST is added to that price.
So amount of GST added in dress purchased by Rehana $ = 12\% \, \times \,x = \dfrac{{12}}{{100}}x$
The total amount to buy a dress for Rehana is equal to sum of actual price and GST price added.
Here, actual price is $x$ and GST added is $\dfrac{{12}}{{100}}x$
The total amount becomes $ = x + \dfrac{{12}}{{100}}x$
So total amount of dress purchased by Rehana is $x + \dfrac{{12}}{{100}}x$
$ = \dfrac{{100x + 12x}}{{100}} = \dfrac{{112x}}{{100}}$
An also it is given in question that Rehana spend Rs. $5400$ to but the dress
So $\dfrac{{112}}{{100}}x = 5400$
$
  x = \dfrac{{100}}{{112}}\left( {5400} \right) \\
  x = 4821.42 \\
 $
So the price before GST was added is Rs. $4821.42$

Note:GST stands for good and service tax which is included as some percentage increase in original cost. Suppose let $x$ be the original cost and if we add $1\% $ GST in it then it’s cost becomes $\left( {x + \dfrac{1}{{100}}x} \right) = \dfrac{{101x}}{{100}}$.