Question

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

Answer 1

Hint: Here the price amount includes VAT means \[{\text{that bill amount has price + VAT}}\]. So, using this trick we will find out the answer for this question. This formula was important to this whole question. Substitute the given values in this formula to find the answer.

Using formula:
${\text{Tax Amount}}$=${\text{VAT}}{\text{percentage}}$$ \times $${\text{Original Price}}$

Complete step-by-step answer:
Given,
Amount paid (Bill amount) = ` $5,400$
VAT = $8\% $percentage
Here we take original price as $x$,
${\text{ = 8% * x}}$${\text{ = }}\dfrac{8}{{100}}{\text{ * x}}$$ = \dfrac{{8x}}{{100}}$
Here Tax amount is $ = \dfrac{{8x}}{{100}}$
Now we will use the above formula here,
${{Tax Amount}}$=${{VAT}}{{percentage}}$$ \times $${{OriginalPrice}}$
Here
\[{\text{Tax Amount = }}\]`$5,400$,
\[{\text{Original price = x}}\],
${\text{Tax amount is = }}\dfrac{{8x}}{{100}}$
Substitute the values in above formula,
$5400 = x + \dfrac{{8x}}{{100}}$
In right hand side we will take lcm,
$5400 = \dfrac{{100x + 8x}}{{100}} = \dfrac{{108x}}{{100}}$
$5400 = \dfrac{{108x}}{{100}}$ value of $x$ is right hand side others are going to left side
\[\dfrac{{5400 \times 100}}{{108}} = x\]
We will simplify the double sides,
$
\Rightarrow \dfrac{{2700 \times 100}}{{54}} = x \\
\Rightarrow \dfrac{{1350 \times 100}}{{27}} = x \\
\Rightarrow \dfrac{{450 \times 100}}{9} = x \\
\Rightarrow 50 \times 100 = x \\
\Rightarrow 5000 = x \\
 $
Original price is 5000
The price of the hair dryer before VAT was added =5000Rs.

Note: We are substituting values in above questions to concentrate the dividend and divisor part. If any problem of changing dividend and divisor values, here completely changing the answer. So, the dividend and divisor part are the most important one in this type of question.