Question

Sudha brought a TV for Rs.13500. If 8% VAT is included in the price, find the original price of TV.

Answer 1

Hint: Subtract the given price by the taxable amount to find original price. The amount of VAT that customer pays is the cost of product less than any of the costs of material used in the product that have already been taxed.
In this question the cost price of the TV is given with a value added tax of 8% this means the cost price of the TV already includes the tax price on the TV, so we will first find the taxable amount of the TV and then we will subtract this amount with the cost price of the TV.

Complete step-by-step answer:
Let the original price of the TV be ‘x.
The cost price of TV for Sudha which includes a 8% VAT \[ = Rs.13500\]
Value added tax on the TV \[ = 8\% \]
Let us assume that the original price of the TV is \[SP = x\]
Now we know the formula
\[SP + VAT\% \times SP = CP\]
Hence by substituting the values the formula, we can write
\[x + 8\% \times x = 13500\]
By further solving this equation we get
\[
  x + \dfrac{8}{{100}} \times x = 13500 \\
   \Rightarrow x + 0.08x = 13500 \\
   \Rightarrow 1.08x = 13500 \\
   \Rightarrow x = \dfrac{{13500}}{{1.08}} \\
   \Rightarrow x = 12500 ;
\]
Hence, we get the original price of the TV\[ = Rs.12500\]
So, the correct answer is “12500 RS”.

Note: Whenever a cost price is given for a good saying inclusive of taxes this means that price is not the original price, it includes some taxable amount so to find the original price we subtract the taxable amount in the cost price.