Question

Shyam buys an article for Rs. $ 10,000 $ and pays $ 7\% $ tax. He sells the same article for Rs. $ 13,000 $ and charges $ 9\% $ tax. Find the VAT paid by Shyam.

Answer 1

Hint: First of all find the percentage of tax paid while purchasing the article and the tax charged while selling an article. Find the difference of the taxes for the resultant value. Convert the percentage given in the form of the fraction with the denominator upon hundred.

Complete step by step solution:
Given that: cost price of an article $ = 10,000 $ Rs.
Tax paid by Shyam $ = 7\% $ of Rs. $ 10,000 $
Here, it suggests the multiplication operation. Convert the percentage in the form of the fraction.
 $ = \dfrac{7}{{100}} \times 10000 $
Find the factors of the terms in the numerator of the above expression -
 $ = \dfrac{7}{{100}} \times 100 \times 100 $
Common factors from the numerator and the denominator cancels each other and therefore remove
 $ = 7 \times 100 $
Simplify the above expression finding the product of the terms –
Tax paid by Shyam $ = 700 $ Rs. ….. (A)
Selling price of the article $ = 13,000 $
Tax charged at $ 9\% = 9\% $ of Rs. $ 13,000 $
Express the above terms in the mathematical expression –
 $ = \dfrac{9}{{100}} \times 13000 $
Find the factors of the terms in the numerator of the above expression -
 $ = \dfrac{9}{{100}} \times 130 \times 100 $
Common factors from the numerator and the denominator cancels each other and therefore remove
 $ = 9 \times 130 $
Find the product of the terms in the above expression –
Tax charged $ = Rs.1,170 $ …… (B)
VAT is defined as the tax recovered on sale and the tax paid on the purchase.
VAT $ = 1170 - 700 $ Rs.
Find the difference of the terms of the above expression –
VAT $ = 470 $ Rs.
Hence, the VAT paid by Shyam is $ 470 $ Rs.
So, the correct answer is “$ 470 $ Rs.”.

Note: Be careful while simplifying mathematical expressions and always remember when its percentage is always with respect to hundred. Always remember that percentage is always based on $ 100\% $ Be good in multiples and the division and remove common factors from the numerator and the denominator for the simplified form.