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Anjana buys a purse for Rs.523.80 including 8% VAT. Find the new selling price of the purse if VAT increases to 10%.

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Hint: Value Added Tax(VAT)
Sales tax is charged by the government on the selling price of an item and is included in the bill amount. Sales tax has been replaced by a new tax called Value Added Tax (VAT). Normally, VAT is included in the price of items like groceries.
Selling Price with VAT = Selling Price + VAT%...................(1)

Complete step-by-step answer:
It is given that a retailer's Anjana sells the product at Rs. 523.80, thus Selling Price including the VAT of the purse = Rs. 523.80.
The VAT already included = 8%
This means that SP with VAT = SP + 0.08SP.
Using the formula (1) from the hint: -
$
   \Rightarrow 523.80 = x + \dfrac{8}{{100}}x \\
   \Rightarrow 523.80 = \dfrac{{100x + 8x}}{{100}} \\
   \Rightarrow \dfrac{{108x}}{{100}} = 523.80 \\
 $
Restating this we have SP with VAT = 1.8SP.
$
   \Rightarrow x = 523.80{\times}\dfrac{{100}}{{108}} \\
   \Rightarrow x = \dfrac{{52380}}{{108}} \\
   \Rightarrow x = 485 \\
 $
Which means SP = Rs. 485
So, original selling price is Rs 485
It's given that a retailer's Anjana originally sold the product at Rs. 485, thus Selling Price of the purse = Rs. 485.
New selling price after 10% VAT
This means that SP with VAT = SP + 0.01SP.
Using the formula (1) from the hint: -
\[
   \Rightarrow New\;Selling\;\Pr ice = 485 + 485\dfrac{{10}}{{100}} \\
   \Rightarrow New\;Selling\;\Pr ice = 485 + 48.50 \\
   \Rightarrow New\;Selling\;\Pr ice = 533.50 \\
 \]
New selling price is Rs. 533.50

Note: VAT is not a part of selling price. Although it is calculated on the selling price it is excluded from the selling price while calculating profit or loss.
A selling price is the amount that a customer will pay to buy a product. If a retailer wants to earn a positive gross margin (or gross profit percentage), the selling price must include an additional amount that is added to the retailer's cost of the product. This additional amount must be sufficient to cover the retailer's selling, general and administrative expenses and some profit which will be additional to the VAT but has to be added before VAT.