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

## Question

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

## 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 \(\rm{Rs}\, 5000\)