Question

Vijay purchased the hair dryer for $Rs5400$ including the $8\% $ VAT. Find the price before the VAT was added.

Answer 1

Hint:Here VAT means the value added tax. So let us assume that the price before the VAT was $Rs{\text{ }}x$ and so if they include the $8\% $ tax, then the additional amount to pay will be $8\% {\text{ of }}x$ which means$\dfrac{{8x}}{{100}}$. So the total amount which is $Rs5400$ will be equal to the sum of price before the VAT and the additional tax added.

Complete step-by-step answer:
Here in this question, it is given that Vijay purchased the hair dryer for $Rs5400$ including the $8\% $ VAT.
So now VAT means the value added tax which includes every kind of taxes and it is the consumption that is added to the price. For example: If the initial price of the article is something, then its shipping cost, GST and every other charge is included in the value added tax which is called VAT.
For example: If some article has a cost of $Rs1000$ and we have $10\% $ VAT then its final price will be
$Rs1000{\text{ + additional tax}}$ and that additional tax will be given by $10\% {\text{ of }}1000$
$\dfrac{{10}}{{100}}(1000) = Rs100$
So the final cost of that article becomes $Rs(1000 + 100) = Rs1100$
We know that its actual price was $Rs1000$ and then $Rs100$ will be the value added tax and here in the above problem, Vijau purchased the hair dryer for $Rs5400$ including $8\% $ VAT.
So this is the final cost of the hair dryer which is $Rs5400$ and we assumed the actual price be $Rs{\text{ }}x$
So the additional amount will be $Rs(8\% {\text{ of }}x)$
And this $Rs(8\% {\text{ of }}x)$ will be the value added tax and we know the total cost and we know that the cost price will be equal to the sum of the actual cost and the additional tax.
So $Rs5400 = Rs{\text{ }}x + Rs(8\% {\text{ of }}x)$
$5400 = x + \dfrac{{8x}}{{100}}$
$5400 = \dfrac{{100x + 8x}}{{100}}$
$5400 = \dfrac{{108x}}{{100}}$
$x = \dfrac{{540000}}{{108}} = Rs5000$
So the price before the VAT would be $Rs5000$ and the VAT added was $Rs400$

Note:: We usually see the sale in the shop of $10\% $ discount of the price that means if the actual price of the article was $Rs{\text{ }}x$, then you can get $10\% $ off on that price.This will be $x - 10\% {\text{ of }}(x)$ and here the discount is $10\% {\text{ of }}x$