Class 10: Sales Tax and VAT

$\displaystyle \textbf{Question 1: } \text{A person purchases a wristwatch costing Rs. }540.\text{ The rate of Sales Tax}$
$\displaystyle \text{is }8\%.\text{ Find the total amount paid by the person for the watch.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Sales price of the wristwatch}=\text{Rs. }540$
$\displaystyle \text{Sales Tax}=8\%\text{ of Rs. }540=\frac{8}{100}\times540=\text{Rs. }43.20$
$\displaystyle \text{Total amount paid}=\text{Rs. }540+\text{Rs. }43.20=\text{Rs. }583.20$
$\\$

$\displaystyle \textbf{Question 2: } \text{A person paid Rs. }345.60\text{ as Sales Tax on a purchase of}$
$\displaystyle \text{Rs. }3840.\text{ Find the rate of Sales Tax.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Sales price of the article}=\text{Rs. }3840$
$\displaystyle \text{Let the rate of Sales Tax}=x\%$
$\displaystyle \therefore \frac{x}{100}\times3840=345.60$
$\displaystyle x=\frac{345.60\times100}{3840}=9$
$\displaystyle \therefore \text{Rate of Sales Tax}=9\%$
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$\displaystyle \textbf{Question 3: } \text{The price of a washing machine, inclusive of Sales Tax, is}$
$\displaystyle \text{Rs. }13530.\text{ If the Sales Tax is }10\%,\text{ find its basic cost price.}\hfill \text{[ICSE 2003]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the basic cost price of the washing machine}=\text{Rs. }x$
$\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }x=\frac{10}{100}x$
$\displaystyle \therefore x+\frac{10}{100}x=13530$
$\displaystyle \frac{110x}{100}=13530$
$\displaystyle x=\frac{13530\times100}{110}=\text{Rs. }12300$
$\displaystyle \therefore \text{Basic cost price of the washing machine}=\text{Rs. }12300$
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$\displaystyle \textbf{Question 4: } \text{A person purchases biscuits costing Rs. }158\text{ on which the rate of}$
$\displaystyle \text{Sales Tax is }6\%.\text{ That person also purchases cosmetic goods costing}$
$\displaystyle \text{Rs. }354\text{ on which the rate of Sales Tax is }9\%.\text{ Find the total}$
$\displaystyle \text{amount to be paid by the person.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Sales price of the biscuits}=\text{Rs. }158$
$\displaystyle \text{Sales Tax}=6\%\text{ of Rs. }158=\frac{6}{100}\times158=\text{Rs. }9.48$
$\displaystyle \text{Sales price of the cosmetic goods}=\text{Rs. }354$
$\displaystyle \text{Sales Tax}=9\%\text{ of Rs. }354=\frac{9}{100}\times354=\text{Rs. }31.86$
$\displaystyle \text{Total amount paid}=\text{Rs. }(158+9.48)+\text{Rs. }(354+31.86)=\text{Rs. }553.34$
$\\$

$\displaystyle \textbf{Question 5: } \text{A person purchases an article costing Rs. }5460.\text{ The shopkeeper}$
$\displaystyle \text{charged Sales Tax at }8\%.\text{ As the person wanted to take the article}$
$\displaystyle \text{outside the State, the shopkeeper charged }3\%\text{ as Central Sales Tax}$
$\displaystyle \text{on the actual price of the article. Find the total amount paid.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Sales price of the article}=\text{Rs. }5460$
$\displaystyle \text{Sales Tax}=8\%\text{ of Rs. }5460=\frac{8}{100}\times5460=\text{Rs. }436.80$
$\displaystyle \text{Central Sales Tax}=3\%\text{ of Rs. }5460=\frac{3}{100}\times5460=\text{Rs. }163.80$
$\displaystyle \text{Total tax}=436.80+163.80=\text{Rs. }600.60$
$\displaystyle \text{Total amount paid}=\text{Rs. }5460+\text{Rs. }600.60=\text{Rs. }6060.60$
$\\$

$\displaystyle \textbf{Question 6: } \text{The marked price of two articles A and B together is}$
$\displaystyle \text{Rs. }6000.\text{ The Sales Tax on article A is }8\%\text{ and that on article B}$
$\displaystyle \text{is }10\%.\text{ If the total Sales Tax collected is Rs. }552,\text{ find the}$
$\displaystyle \text{marked price of each article.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the marked price of article A}=\text{Rs. }x$
$\displaystyle \text{Then the marked price of article B}=\text{Rs. }(6000-x)$
$\displaystyle \text{Sales Tax on A}=\frac{8}{100}x,\qquad \text{Sales Tax on B}=\frac{10}{100}(6000-x)$
$\displaystyle \therefore \frac{8}{100}x+\frac{10}{100}(6000-x)=552$
$\displaystyle 8x+60000-10x=55200$
$\displaystyle -2x=-4800$
$\displaystyle x=2400$
$\displaystyle \therefore \text{Marked price of article A}=\text{Rs. }2400$
$\displaystyle \text{Marked price of article B}=6000-2400=\text{Rs. }3600$
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$\displaystyle \textbf{Question 7: } \text{A person buys a leather coat costing Rs. }3600,\text{ the rate of}$
$\displaystyle \text{Sales Tax being }10\%.\text{ She asks the shopkeeper to reduce the price}$
$\displaystyle \text{of the coat so that she does not have to pay more than Rs. }3366$
$\displaystyle \text{including Sales Tax. Calculate:}$
$\displaystyle \text{(i) Reduction needed in the cost price of the coat.}$
$\displaystyle \text{(ii) Reduction as a percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Original sales price of the leather coat}=\text{Rs. }3600$
$\displaystyle \text{Let the reduced sales price of the coat}=\text{Rs. }x$
$\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }x=\frac{10}{100}x$
$\displaystyle \text{Total amount paid}=x+\frac{10}{100}x=3366$
$\displaystyle \frac{110x}{100}=3366$
$\displaystyle x=\frac{3366\times100}{110}=\text{Rs. }3060$
$\displaystyle \text{Reduction in price}=3600-3060=\text{Rs. }540$
$\displaystyle \%\text{ Reduction}=\frac{540}{3600}\times100=15\%$
$\\$

$\displaystyle \textbf{Question 8: } \text{The price of a T.V. set inclusive of Sales Tax of }9\%$
$\displaystyle \text{is Rs. }13407.\text{ Find its marked price. If Sales Tax is increased}$
$\displaystyle \text{to }13\%,\text{ how much more does the customer have to pay for the}$
$\displaystyle \text{T.V.?}\hfill \text{[ICSE 2002]}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the marked price of the T.V.}=\text{Rs. }x$
$\displaystyle \text{Price inclusive of }9\%\text{ Sales Tax}=13407$
$\displaystyle x+\frac{9}{100}x=13407$
$\displaystyle \frac{109x}{100}=13407$
$\displaystyle x=\frac{13407\times100}{109}=\text{Rs. }12300$
$\displaystyle \therefore \text{Marked price of the T.V.}=\text{Rs. }12300$
$\displaystyle \text{Sales Tax at }13\%=\frac{13}{100}\times12300=\text{Rs. }1599$
$\displaystyle \text{Sales Tax at }9\%=\frac{9}{100}\times12300=\text{Rs. }1107$
$\displaystyle \text{Additional amount to be paid}=1599-1107=\text{Rs. }492$
$\\$

$\displaystyle \textbf{Question 9: } \text{The price of an article is Rs. }8250\text{ which includes Sales Tax}$
$\displaystyle \text{at }10\%.\text{ Find how much more or less a customer pays if the Sales Tax:}$
$\displaystyle \text{(i) Increases to }15\%\qquad\text{(ii) Decreases to }6\%$
$\displaystyle \text{(iii) Increases by }2\%\qquad\text{(iv) Decreases by }3\%$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total price of the article}=\text{Rs. }8250$
$\displaystyle \text{Let the basic price of the article}=\text{Rs. }x$
$\displaystyle x+\frac{10}{100}x=8250$
$\displaystyle \frac{110x}{100}=8250$
$\displaystyle x=\frac{8250\times100}{110}=\text{Rs. }7500$
$\displaystyle \text{Sales Tax at }10\%=10\%\text{ of Rs. }7500=\text{Rs. }750$
$\displaystyle \text{(i) Additional amount when Sales Tax becomes }15\%=\frac{5}{100}\times7500=\text{Rs. }375\text{ more}$
$\displaystyle \text{(ii) Reduction when Sales Tax becomes }6\%=\frac{4}{100}\times7500=\text{Rs. }300\text{ less}$
$\displaystyle \text{(iii) Additional amount when Sales Tax increases by }2\%=\frac{2}{100}\times7500=\text{Rs. }150\text{ more}$
$\displaystyle \text{(iv) Reduction when Sales Tax decreases by }3\%=\frac{3}{100}\times7500=\text{Rs. }225\text{ less}$
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$\displaystyle \textbf{Question 10: } \text{A bicycle is available for Rs. }1664\text{ including Sales Tax.}$
$\displaystyle \text{If the list price of the bicycle is Rs. }1600,\text{ find:}$
$\displaystyle \text{(i) The rate of Sales Tax.}\qquad\text{(ii) The price a customer will pay if}$
$\displaystyle \text{the Sales Tax is increased by }6\%.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total price of the bicycle}=\text{Rs. }1664$
$\displaystyle \text{List price of the bicycle}=\text{Rs. }1600$
$\displaystyle \text{Sales Tax paid}=1664-1600=\text{Rs. }64$
$\displaystyle \text{Rate of Sales Tax}=\frac{64}{1600}\times100=4\%$
$\displaystyle \text{New rate of Sales Tax}=4\%+6\%=10\%$
$\displaystyle \text{Sales Tax at the new rate}=10\%\text{ of Rs. }1600=\text{Rs. }160$
$\displaystyle \text{Price to be paid}=1600+160=\text{Rs. }1760$
$\\$

Question 11: When the rate of Sale-tax is decreased from 9% to 6% for a colored T.V. a person will save Rs. 780 in buying this T.V. Find the list price of the T.V.

Answer:

Let Sales Price of the T.V. $\displaystyle = \text{ Rs. } x$

$\displaystyle \text{Saving on Sales Tax } = \frac{3}{100} \times x = 780 \Rightarrow x = \text{ Rs. } 26000$

$\displaystyle \\$

$\displaystyle \textbf{Question 12: } \text{A shopkeeper sells an article for Rs. }21384\text{ including}$
$\displaystyle \text{10\% Sales Tax. However, the actual rate of Sales Tax is }8\%.$
$\displaystyle \text{Find the extra profit made by the dealer.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total amount paid}=\text{Rs. }21384$
$\displaystyle \text{Let the selling price of the article (before Sales Tax)}=\text{Rs. }x$
$\displaystyle x+\frac{10}{100}x=21384$
$\displaystyle \frac{110x}{100}=21384$
$\displaystyle x=\frac{21384\times100}{110}=\text{Rs. }19440$
$\displaystyle \text{The dealer charged Sales Tax at }10\%\text{ instead of }8\%$
$\displaystyle \text{Extra profit}=(10\%-8\%)\text{ of Rs. }19440$
$\displaystyle =\frac{2}{100}\times19440=\text{Rs. }388.80$
$\\$