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Question
Shruti bought a set of cosmetic items for Rs 345 including 15% value added tax and a purse for Rs 110 including 10% VAT. What percent is the VAT charged on the whole transaction?
Solution
\[\text { Let the price of the cosmetic items be Rs . x and the price of the purse be Rs . y } . \]
\[\text { VAT = 15 % of x } = \frac{15x}{100} = Rs . \frac{3x}{20}\]
\[\text { VAT = 10 % of y } = \frac{10y}{100} = Rs . \frac{y}{10}\]
\[\text { So, SP of cosmetic items = x } + \frac{3x}{20} = Rs . \frac{23x}{20}\]
\[\text { SP of purse = } \left( y + \frac{y}{10} \right) = Rs . \frac{11y}{10}\]
\[\text { But the selling price of the cosmetic items and the purse is Rs . 345 and Rs . 110 respectively . } \]
\[\text { So }, \frac{23x}{20} = 345\]
\[\text { x = Rs }. 300\]
\[\text { and }\]
\[\frac{11y}{10} = 110\]
\[11y = 1100\]
\[y = Rs . 100\]
\[Total price = Rs . (300 + 100) = Rs . 400\]
\[Now, \]
\[\text { Let the VAT on the whole transaction be r % } . \]
\[\text { r % of 400 = } \frac{r}{100} \times 400 = 4r\]
\[\text { Total transaction = Rs . 345 + 110 = Rs }. 455\]
\[\text { So }, \]
\[4r + 400 = 455\]
\[4r = 55\]
\[r = \frac{55}{4}\]
\[ = 13 . 75\]
\[\text { Thus, VAT charged on the whole transaction is 13 . 75 % } .\]
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