Question

A ceiling fan was bought for $Rs.1375$ including $10\% $ VAT. What was the selling price of the fan?

Answer 1

Hint: The amount given by the customer contains the actual selling price and the value added tax. It is given that the percent of VAT is $10$. So we can calculate the selling price and tax amount separately. Thus we can find the answer.

Formula used: For any $x,y$ we have,
$x\% {\text{ of y = }}\dfrac{x}{{100}} \times y$

Complete step-by-step answer:
It is given that the ceiling fan was bought for $Rs.1375$. This amount includes the VAT (Value added tax). We are asked to find the actual selling price.
Since it is given that the value added tax is $10\% $, we can say that $Rs.1375$ is the sum of selling price and $10\% $ of the selling price.
Let the selling price be $SP$.
So we can write as,
${\text{SP}} + 10\% {\text{ of SP = 1375}}$
For any $x,y$ we have,
$x\% {\text{ of y = }}\dfrac{x}{{100}} \times y$
$\Rightarrow$$SP + \dfrac{{10SP}}{{100}} = 1375$
Simplifying the above equation we get,
$\Rightarrow$$SP + \dfrac{{SP}}{{10}} = 1375$
Multiplying both sides of the equation by we get,
$\Rightarrow$$10 S.P + S.P$ =$1375 \times 10$
$\Rightarrow$$11 S.P = 13750$
Dividing $10$ the above equation by$11$ we get as,
$ \Rightarrow SP = \dfrac{{13750}}{{11}} = 1250$
This gives the selling price as $Rs.1250$.
Also the tax is $10\% $ of the selling price, which will be equal to $125$.
So we get the amount paid by the customer as $1250 + 125 = 1375$.

$\therefore $ The selling price is $Rs.1250$.

Note: We can solve this problem simply in another way.
Since the VAT is $10\% $ of the selling price, the amount the customer has to pay will be $110\% $ of the selling price.
This gives , ${\text{110\% of SP = 1375}}$
$\dfrac{{110}}{{100}} \times SP = 1375$
Simplifying the above equation we get,
$ \Rightarrow SP = \dfrac{{1375 \times 100}}{{110}} = 1250$
So we get the actual selling price as $Rs.1250$.