Question

A shopkeeper sells an article at the listed price of Rs. 1500 and the rate of VAT is 12% at each stage of sale. If the shopkeeper pays a VAT of Rs. 36 to the government, what was the price, inclusive of Tax, at which the shopkeeper purchased the article from the wholesaler?

Answer 1

Hint: Assume the cost price (C.P) of the article as x. In the first step find the VAT of the article on its selling price by calculating 12% of Rs. 1500. Now, calculate the vat on the cost price by finding 12% of x. Subtract VAT of selling price from the VAT of cost price and equate it with 36. Find the value of x to get the C.P. Finally, add x with 12% of x to get the cost price inclusive of Tax.

Complete step by step answer:
Here we have been provided with the selling price of an article as Rs. 1500 with the rate of VAT equal to 12% at each stage of sale. We have to determine the cost at which the shopkeeper purchased the article, including tax, if he pays Rs. 36 as the VAT to the government.
Now, VAT means Value Added Tax. It is equal to the difference in tax that a shopkeeper charges from the customer and the tax he paid to buy an article. So let us assume the cost price of the article as x.
$\Rightarrow $ VAT on the selling price of the article = 12% of 1500
$\Rightarrow $ VAT on the selling price of the article = $\dfrac{12}{100}\times 1500$ = Rs. 180
Also, VAT on the cost price = 12% of x
$\Rightarrow $ VAT on the cost price of the article = \[\dfrac{12}{100}\times x=\dfrac{12x}{100}\]
So, the VAT paid by the shopkeeper to the government = VAT he will charge from the customer – VAT he paid to the wholesaler for purchasing the article, so we have,
$\Rightarrow 36=180-\dfrac{12x}{100}$
Solving for the value of x we get,
$\Rightarrow x=1200$
So the cost price of the article is Rs. 1200 and the tax on it will be 12% of 1200. Therefore we have,
$\Rightarrow $ Cost price of the article including Tax = 1200 + 12% of 1200
$\Rightarrow $ Cost price of the article including Tax = 1200 + 144 = Rs. 1344

Hence, the shopkeeper purchased the article at Rs. 1344 from the wholesaler.

Note: : You must remember the definition of VAT, what it means mathematically and how to calculate it. Without understanding these terms we cannot solve the above question. You may see that here the shopkeeper will have gained as he is selling the article at a price higher than the cost price. Remember the formula to calculate VAT on an article