Class 10: Sales Tax and Value Added Tax

$\displaystyle \textbf{Question 1: } \text{A person purchased a pair of shoes costing Rs. }850.$
$\displaystyle \text{Calculate the total amount to be paid if Sales Tax is }6\%.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Sales Tax}=6\%\text{ of Rs. }850=\frac{6}{100}\times850=\text{Rs. }51$
$\displaystyle \therefore \text{Total amount paid}=850+51=\text{Rs. }901$
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$\displaystyle \textbf{Question 2: } \text{Mr. Gupta purchased an article for Rs. }702\text{ including}$
$\displaystyle \text{Sales Tax at }8\%.\text{ Find the sale price.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the sale price be Rs. }x$
$\displaystyle x+\frac{8}{100}x=702$
$\displaystyle \frac{108x}{100}=702$
$\displaystyle x=\frac{702\times100}{108}=\text{Rs. }650$
$\displaystyle \therefore \text{Sale price}=\text{Rs. }650$
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$\displaystyle \textbf{Question 3: } \text{A face cream costs Rs. }79.10\text{ including tax. If the}$
$\displaystyle \text{printed price is Rs. }70,\text{ find the rate of tax.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Tax}=79.10-70=\text{Rs. }9.10$
$\displaystyle \text{Rate of tax}=\frac{9.10}{70}\times100=13\%$
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$\displaystyle \textbf{Question 4: } \text{Goods costing Rs. }165\text{ are taxed at }6\%\text{ and goods}$
$\displaystyle \text{costing Rs. }230\text{ are taxed at }10\%.\text{ If Rs. }500\text{ is paid, find}$
$\displaystyle \text{the balance.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Amount payable for first goods}=165+\frac{6}{100}\times165=\text{Rs. }174.90$
$\displaystyle \text{Amount payable for second goods}=230+\frac{10}{100}\times230=\text{Rs. }253$
$\displaystyle \text{Total amount paid}=174.90+253=\text{Rs. }427.90$
$\displaystyle \therefore \text{Balance}=500-427.90=\text{Rs. }72.10$
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$\displaystyle \textbf{Question 5: } \text{An article is marked at Rs. }2200.\text{ The rate of Sales Tax is }12\%.$
$\displaystyle \text{If the final amount paid is not more than Rs. }2240,\text{ find the reduction percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the reduced price be Rs. }x$
$\displaystyle x+\frac{12}{100}x=2240$
$\displaystyle \frac{112x}{100}=2240$
$\displaystyle x=\frac{2240\times100}{112}=\text{Rs. }2000$
$\displaystyle \text{Reduction}=2200-2000=\text{Rs. }200$
$\displaystyle \text{Reduction }\%=\frac{200}{2200}\times100=9\frac{1}{11}\%$
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$\displaystyle \textbf{Question 6: } \text{Price inclusive of }12\%\text{ Sales Tax is Rs. }2016.\text{ Find the}$
$\displaystyle \text{marked price and the new price if Sales Tax is }7\%.$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the marked price be Rs. }x$
$\displaystyle x+\frac{12}{100}x=2016$
$\displaystyle \frac{112x}{100}=2016$
$\displaystyle x=\frac{2016\times100}{112}=\text{Rs. }1800$
$\displaystyle \text{New price}=1800+\frac{7}{100}\times1800=\text{Rs. }1926$
$\displaystyle \text{Difference}=2016-1926=\text{Rs. }90$
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$\displaystyle \textbf{Question 7: } \text{An article costs Rs. }3600\text{ and overhead expenses are Rs. }1200.$
$\displaystyle \text{If profit is }15\%\text{ and Sales Tax is }8\%,\text{ find the customer price.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Total cost price}=3600+1200=\text{Rs. }4800$
$\displaystyle \text{Selling price}=4800+\frac{15}{100}\times4800=\text{Rs. }5520$
$\displaystyle \text{Sales Tax}=8\%\text{ of Rs. }5520=\frac{8}{100}\times5520=\text{Rs. }441.60$
$\displaystyle \therefore \text{Customer price}=5520+441.60=\text{Rs. }5961.60$
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$\displaystyle \textbf{Question 8: } \text{An article costs Rs. }1500\text{ and expenses are }20\%\text{ of the cost.}$
$\displaystyle \text{It is sold for Rs. }2452.50\text{ including }9\%\text{ Sales Tax. Find the profit percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the selling price before Sales Tax be Rs. }x$
$\displaystyle x+\frac{9}{100}x=2452.50$
$\displaystyle \frac{109x}{100}=2452.50$
$\displaystyle x=\frac{2452.50\times100}{109}=\text{Rs. }2250$
$\displaystyle \text{Total cost price}=1500+\frac{20}{100}\times1500=\text{Rs. }1800$
$\displaystyle \text{Profit}=2250-1800=\text{Rs. }450$
$\displaystyle \text{Profit }\%=\frac{450}{1800}\times100=25\%$
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$\displaystyle \textbf{Question 9: } \text{A computer is marked at Rs. }45000.\text{ Two successive discounts}$
$\displaystyle \text{of }7\%\text{ and }4\%\text{ are given. If Sales Tax is }8\%,\text{ find the tax}$
$\displaystyle \text{and the final price.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Marked price of the computer}=\text{Rs. }45000$
$\displaystyle \text{Price after }7\%\text{ discount}=\frac{93}{100}\times45000=\text{Rs. }41850$
$\displaystyle \text{Price after further }4\%\text{ discount}=\frac{96}{100}\times41850=\text{Rs. }40176$
$\displaystyle \text{Sales Tax}=8\%\text{ of Rs. }40176=\frac{8}{100}\times40176=\text{Rs. }3214.08$
$\displaystyle \therefore \text{Final price}=40176+3214.08=\text{Rs. }43390.08$
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$\displaystyle \textbf{Question 10: } \text{A person paid Rs. }1374\text{ after }15\%\text{ discount and }10\%$
$\displaystyle \text{Sales Tax. Find the marked price.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the marked price be Rs. }x$
$\displaystyle x\times\frac{85}{100}\times\frac{110}{100}=1374$
$\displaystyle x=\frac{1374\times100\times100}{85\times110}=\text{Rs. }1470$
$\displaystyle \therefore \text{Marked price}=\text{Rs. }1470$
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$\displaystyle \textbf{Question 11: } \text{An article is bought at }20\%\text{ rebate. Rs. }40\text{ is spent}$
$\displaystyle \text{on expenses. It is sold for Rs. }1070\text{ including }7\%\text{ Sales Tax.}$
$\displaystyle \text{Find the gain percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the selling price before Sales Tax be Rs. }x$
$\displaystyle x+\frac{7}{100}x=1070$
$\displaystyle \frac{107x}{100}=1070$
$\displaystyle x=\frac{1070\times100}{107}=\text{Rs. }1000$
$\displaystyle \text{Cost price after }20\%\text{ rebate}=\frac{80}{100}\times1000=\text{Rs. }800$
$\displaystyle \text{Total cost price}=800+40=\text{Rs. }840$
$\displaystyle \text{Profit}=1000-840=\text{Rs. }160$
$\displaystyle \text{Profit }\%=\frac{160}{840}\times100=19\frac{1}{21}\%$
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$\displaystyle \textbf{Question 12: } \text{The printed price of an article is Rs. }2000.\text{ It is purchased}$
$\displaystyle \text{at a discount of }30\%.\text{ If the rate of VAT is }8\%,\text{ find the VAT paid.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Printed price}=\text{Rs. }2000$
$\displaystyle \text{Purchase price after }30\%\text{ discount}=\frac{70}{100}\times2000=\text{Rs. }1400$
$\displaystyle \text{Input VAT}=8\%\text{ of Rs. }1400=\frac{8}{100}\times1400=\text{Rs. }112$
$\displaystyle \text{Output VAT}=8\%\text{ of Rs. }2000=\frac{8}{100}\times2000=\text{Rs. }160$
$\displaystyle \therefore \text{VAT paid}=160-112=\text{Rs. }48$
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$\displaystyle \textbf{Question 13: } \text{The marked price of an article is Rs. }7500.\text{ If the rate of}$
$\displaystyle \text{VAT is }12\%\text{ and the VAT paid is Rs. }180,\text{ find the cost price}$
$\displaystyle \text{inclusive of tax.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Output VAT}=12\%\text{ of Rs. }7500=\frac{12}{100}\times7500=\text{Rs. }900$
$\displaystyle \text{Input VAT}=900-180=\text{Rs. }720$
$\displaystyle \frac{12}{100}\times x=720$
$\displaystyle x=\frac{720\times100}{12}=\text{Rs. }6000$
$\displaystyle \text{Cost price inclusive of VAT}=6000+720=\text{Rs. }6720$
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$\displaystyle \textbf{Question 14: } \text{An article is purchased for Rs. }10000\text{ with Sales Tax at }7\%$
$\displaystyle \text{and sold for Rs. }13000\text{ with Sales Tax at }9\%.\text{ Find the VAT paid.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Input VAT}=7\%\text{ of Rs. }10000=\frac{7}{100}\times10000=\text{Rs. }700$
$\displaystyle \text{Output VAT}=9\%\text{ of Rs. }13000=\frac{9}{100}\times13000=\text{Rs. }1170$
$\displaystyle \therefore \text{VAT paid}=1170-700=\text{Rs. }470$
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$\displaystyle \textbf{Question 15: } \text{Manufacturer sells an article for Rs. }22000\text{ including tax.}$
$\displaystyle \text{Find the price and retailer's VAT.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The question is incomplete. The tax rate is inferred as }10\%,\text{ but the retailer's}$
$\displaystyle \text{selling price is required to calculate the retailer's VAT.}$
$\displaystyle \text{If tax rate is }10\%,\text{ then let the price before tax be Rs. }x$
$\displaystyle x+\frac{10}{100}x=22000$
$\displaystyle \frac{110x}{100}=22000$
$\displaystyle x=\frac{22000\times100}{110}=\text{Rs. }20000$
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$\displaystyle \textbf{Question 16: } \text{Printed price is Rs. }60000,\text{ discount is }20\%\text{ and tax is }6\%.$
$\displaystyle \text{Find costs and VAT.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{The question is incomplete, but assuming the shopkeeper buys at }20\%\text{ discount}$
$\displaystyle \text{and sells at printed price, the solution is:}$
$\displaystyle \text{Cost price before tax}=\frac{80}{100}\times60000=\text{Rs. }48000$
$\displaystyle \text{Tax paid by the shopkeeper}=6\%\text{ of Rs. }48000=\text{Rs. }2880$
$\displaystyle \text{Cost to shopkeeper including tax}=48000+2880=\text{Rs. }50880$
$\displaystyle \text{Selling price before tax}=\text{Rs. }60000$
$\displaystyle \text{Tax charged to customer}=6\%\text{ of Rs. }60000=\text{Rs. }3600$
$\displaystyle \text{VAT paid}=3600-2880=\text{Rs. }720$
$\displaystyle \text{Customer cost}=60000+3600=\text{Rs. }63600$
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