Question

A shopkeeper sells a washing machine for Rs.$9000$ including VAT. What is the marked price if the rate of VAT is $12.5\% $ ?

Answer 1

Hint: The selling price of the washing machine includes all the taxes, so first assume the marked price of the washing machine and then find the cost of VAT on the marked price. After that, use them to find the required result.

Complete step by step solution:
It is given that the selling price of the washing machine is Rs.$9000$, which includes VAT of 12.5%. Now, assume that the marked price of the washing machine is$x$. It is also given that the rate of VAT is $12.5\% $.
Now first, find the cost of VAT on the marked price of the washing machine.
So, find$12.5\% $ of the marked price, which is the VAT on the marked price.
$12.5\% {\text{ of }}x = \dfrac{{12.5}}{{100}} \times x$
Simplify the result:
$12.5\% {\text{ of }}x = \dfrac{{125x}}{{1000}}$
We know that the sum of the marked price and VAT is the selling price of the washing machine and the selling price of the machine is given in the problem as Rs.$9000$. The formula for the relation of the marked price, VAT, and selling price is given by:
${\text{Selling price}} = {\text{Marked price}} + {\text{VAT}}$
Substitute the selling price as Rs.$9000$, VAT as$\dfrac{{125x}}{{1000}}$ and marked price as $x$in the above equation.
$9000 = x + \dfrac{{125x}}{{1000}}$
Solve the above equation for the value of$x$, which defines the marked price of the washing machine.
$ \Rightarrow 9000 = \dfrac{{1000x + 125x}}{{1000}}$
$ \Rightarrow 9000 \times 1000 = 1125x$
$ \Rightarrow \dfrac{{9000 \times 1000}}{{1125}} = x$
Simplify the above expression for getting the value of $x$.
$x = 8000$

Therefore, the marked price of the washing machine is$Rs.8000$if the rate of VAT is$12.5\% $.

Note: The sum of marked price and VAT tax on the marked price is equal to the selling price of the washing machine. The rate of VAT is given to be $12.5\% $, then first find the cost of VAT, by finding the $12.5\% $ of marked price.