Question

I purchased a hair-dryer for 5,400 included $8\% $VAT. Find the price before VAT was added.

Answer 1

Hint: As VAT means value added tax i.e. amount of tax added to the actual value of the object. So, if we have to calculate the object price before VAT is added, we have to subtract that percentage from the final selling price i.e. $8\% $ of the price of the object before VAT is subtracted from the final selling price.

Complete step-by-step answer:
Here, we have given the selling price including VAT i.e.
$ \Rightarrow S.P = Rs.5400$
Vat percentage is given to us i.e. $8\% $, so in the selling price of the object it is included.
We have to find the price of the object before VAT. Let the price of the object be x. Selling price of the object after VAT is the sum of x and $8\% $of x i.e.
$ \Rightarrow S.P = x + 8\% \times x$
Here we know S.P and putting the value of S.P we get,
$ \Rightarrow 5400 = x + 8\% \times x$
Solve the above equation by converting $8\% $ into fraction we get,
$ \Rightarrow 5400 = x + \dfrac{8}{{100}} \times x$
$ \Rightarrow 5400 = x + \dfrac{8}{{100}}x$
Taking the L.C.M of x terms we get,
$ \Rightarrow 5400 = \dfrac{{100x + 8x}}{{100}}$
By adding the x terms, we get,
$ \Rightarrow 5400 = \dfrac{{108x}}{{100}}$
Taking the x on L.H.S and rest on R.H.S we get,
$ \Rightarrow x = \dfrac{{5400 \times 100}}{{108}}$
By cancelling 5400 with 108 we get,
$ \Rightarrow x = 50 \times 100$
$ \Rightarrow x = Rs.5000$
Hence the value of the object before VAT is added is Rs. 5000.

Note: The common mistake done by students is to take $8\% $ of selling price included VAT and then subtract that $8\% $ from that number. This method is wrong. As VAT is value added tax which is applied on the selling price of the object. So, we will add it to the selling price excluding VAT. $8\% $of 5400 and $8\% $of 5000 are different things. Take care of this thing.
VAT is the type of tax collected by the government on the sale or purchase of goods. In this system the government collects tax at every stage on the product right from the manufacturer to the retailer.