Raza purchased a bicycle for ₹ 6810. He had paid a VAT of 13.5%. The list price of the bicycle was

### Concept & Formula Value Added Tax (VAT) is calculated as a percentage of the list price (or marked price) and is added to it to determine the final selling price paid by the customer. $$Final Price = List Price \times \left(1 + \frac{VAT\%}{100}\right)$$ ### Step-by-Step Solution 1. Let the list price of the bicycle be $x$. 2. The VAT paid is $13.5\%$ of the list price. 3. The total amount paid by Raza is the sum of the list price and the VAT. $$x + 13.5\% \text{ of } x = 6810$$ $$x \left(1 + \frac{13.5}{100}\right) = 6810$$ $$1.135x = 6810$$ 4. Solve for $x$: $$x = \frac{6810}{1.135}$$ Multiply numerator and denominator by 1000 to remove the decimal: $$x = \frac{6810000}{1135}$$ $$x = 6000$$ ### Exam Strategy & Shortcut Treat the list price as $100\%$. With a $13.5\%$ VAT, the final price is $113.5\%$. $113.5\%$ corresponds to $6810$. $1\%$ corresponds to $\frac{6810}{113.5} = 60$. $100\%$ corresponds to $60 \times 100 = 6000$. ### Common Pitfall A common mistake is calculating $13.5\%$ of the final purchasing price (6810) and subtracting it, rather than setting up the equation where VAT is based on the unknown base list price. ### Final Answer Therefore, the correct answer is **₹ 6000**.