Question

Rahana purchased a dress for Rs.5400 including 12% GST. Find the price of the dress before GST.

Answer 1

Hint: The total cost of the purchase is equal to the sum of the cost of the dress and the GST. Goods and Services Tax (GST) is often represented as a part or percentage of the total cost of the purchase. To find the price of the dress before GST, we have to represent the GST in terms of a fraction of the cost of the dress and equate it with the total cost of the purchase.

Complete step by step answer:
We are given that Rahana purchased a dress for an amount of Rs.5400 including GST. We are asked to find the price of the dress before GST.
We know that, The total cost of the purchase = Cost of the dress + GST of the purchase
We are given,
The total cost of the purchase = Rs.5400
We are also given that the GST of the purchase is equal to 12% of the cost of the dress.
Mathematically speaking,
GST of the purchase=12% of cost of the dress
$=\dfrac{12}{100}\times $ (cost of the dress)
Since, total cost of the purchase is equal Rs.5400,
Rs.5400 = Cost of the dress + $\dfrac{12}{100}\times $ (cost of the dress)
Let cost of the dress be C
Then,
5400 = C+ $\dfrac{12}{100}\times $ (C)
Taking LCM,
5400 = $\dfrac{100C}{100}+\dfrac{12C}{100}$
5400 = $\dfrac{112C}{100}$
$\therefore C=\dfrac{5400\times 100}{112}=Rs.4821.4$
$\therefore $ Cost of the dress$=Rs.4821.4$
We know that,
Total cost of the purchase = Cost of the dress + GST of the purchase
$\therefore $ GST of the purchase= Total cost of the purchase - Cost of the dress
$=5400-4821.4$
$=Rs.578.6$

Note:
Percentages are representations of fractions of a whole. In this question, the GST is simply a part of the cost of the dress or ‘the whole’. In this particular question, the GST is 12% of the cost of the dress, that is, $\dfrac{12}{100}$ times the cost. The term ‘x% of A’, simply means ‘$\dfrac{x}{100}$ times A’.