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# Ex.8.2 Q10 Comparing Quantities Solution - NCERT Maths Class 8

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## Question

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

Video Solution
Comparing Quantities
Ex 8.2 | Question 10

## Text Solution

What is known?

Price of hair dryer with VAT $$= \rm{Rs}\, 5400$$

VAT$$\%$$ $$= 8\%$$

What is unknown?

Price of hair dryer before VAT was added

Reasoning:

Assuming initial price of hair dryer as $$x$$ and equating S.P. of a hair dryer plus VAT to $$\rm{Rs}\, 5400$$, value of $$x$$ can be found.

Steps:

Let the initial price of hair dryer be $$\rm{Rs}$$ $$x$$

Price of hair dryer with VAT is $$\rm{Rs}\, 5400$$

VAT % $$=8\%$$

VAT $$= 8\%$$ of initial price of hair dryer

So, initial price of hair dryer $$+$$ VAT $$= 5400$$

\begin{align}x + 8\% \times x &= 5400\\x + \frac{8}{{100}} \times x &= 5400\\\frac{{{108}}}{{{100}}} \times x &= {5400}\\x &= \frac{{{5400 \times 100}}}{{{108}}}\\x &= {\rm{Rs}}\;5000\end{align}

Price of hair dryer before VAT was added is $$\rm{Rs}\, 5000$$

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