In this exercise, all the prices are excluding tax/VAT unless specified.

\displaystyle \textbf{Question 1: } \text{A person purchases a compact computer system for Rs. }47700
\displaystyle \text{which includes }10\%\text{ rebate on the marked price and then }6\%\text{ Sales Tax}
\displaystyle \text{on the remaining price. Find the marked price of the computer.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the marked price of the computer}=\text{Rs. }x
\displaystyle \text{Price after }10\%\text{ rebate}=\frac{90}{100}x
\displaystyle \text{Sales Tax}=6\%\text{ of }\frac{90x}{100}=\frac{6}{100}\times\frac{90x}{100}
\displaystyle \therefore \frac{90x}{100}+\frac{6}{100}\times\frac{90x}{100}=47700
\displaystyle \frac{90x}{100}\times\frac{106}{100}=47700
\displaystyle x=\frac{47700\times100\times100}{90\times106}=\text{Rs. }50000
\displaystyle \therefore \text{Marked price of the computer}=\text{Rs. }50000
\\

\displaystyle \textbf{Question 2: } \text{A wholesaler sells an article for Rs. }2700\text{ at a discount}
\displaystyle \text{of }10\%\text{ on the printed price to a retailer. The retailer raises the}
\displaystyle \text{printed price by }15\%\text{ and sells it for Rs. }3657\text{ including Sales Tax}
\displaystyle \text{on the new marked price. Find:}
\displaystyle \text{(i) The rate of Sales Tax.}
\displaystyle \text{(ii) The profit percent made by the retailer.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the printed price of the article}=\text{Rs. }x
\displaystyle \frac{90}{100}x=2700
\displaystyle x=\frac{2700\times100}{90}=\text{Rs. }3000
\displaystyle \text{New marked price}=3000+\frac{15}{100}\times3000=\text{Rs. }3450
\displaystyle \text{Let the rate of Sales Tax}=r\%
\displaystyle 3450+\frac{r}{100}\times3450=3657
\displaystyle 3450\left(1+\frac{r}{100}\right)=3657
\displaystyle 1+\frac{r}{100}=\frac{3657}{3450}=1.06
\displaystyle r=6
\displaystyle \therefore \text{Rate of Sales Tax}=6\%
\displaystyle \text{Profit}=3450-2700=\text{Rs. }750
\displaystyle \text{Profit }\%=\frac{750}{2700}\times100=27\frac{7}{9}\%
\\

\displaystyle \textbf{Question 3: } \text{A shopkeeper buys an article at }70\%\text{ of its printed price. He}
\displaystyle \text{spends Rs. }40\text{ on transportation. After charging Sales Tax at }10\%
\displaystyle \text{on the printed price, he sells the article for Rs. }7040.\text{ Find his profit}
\displaystyle \text{as a percent to the nearest integer.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the printed price of the article}=\text{Rs. }x
\displaystyle \text{Selling price including Sales Tax}=\text{Rs. }7040
\displaystyle x+\frac{10}{100}x=7040
\displaystyle \frac{110x}{100}=7040
\displaystyle x=\frac{7040\times100}{110}=\text{Rs. }6400
\displaystyle \text{Cost price for the shopkeeper}=70\%\text{ of Rs. }6400+\text{Rs. }40
\displaystyle =\frac{70}{100}\times6400+40=\text{Rs. }4520
\displaystyle \text{Profit}=6400-4520=\text{Rs. }1880
\displaystyle \text{Profit }\%=\frac{1880}{4520}\times100=41.59\%
\displaystyle \therefore \text{Profit percent, to the nearest integer}=42\%
\\

\displaystyle \textbf{Question 4: } \text{A person bought a washing machine marked at Rs. }9375.
\displaystyle \text{The rate of Sales Tax is }6\%.\text{ She asks the shopkeeper to reduce}
\displaystyle \text{the price so that she has to pay Rs. }9275\text{ inclusive of Sales Tax.}
\displaystyle \text{Find the reduction needed in the price of the washing machine.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the reduced price of the washing machine}=\text{Rs. }x
\displaystyle x+\frac{6}{100}x=9275
\displaystyle \frac{106x}{100}=9275
\displaystyle x=\frac{9275\times100}{106}=\text{Rs. }8750
\displaystyle \text{Reduction needed}=9375-8750=\text{Rs. }625
\\

\displaystyle \textbf{Question 5: } \text{The catalog price of a coloured T.V. is Rs. }18000.\text{ The shopkeeper}
\displaystyle \text{sells it at a discount of }20\%\text{ on the catalog price and gives a further}
\displaystyle 10\%\text{ off-season discount on the balance. Sales Tax at }10\%\text{ is charged}
\displaystyle \text{on the remaining amount. Find:}
\displaystyle \text{(i) The Sales Tax amount paid by the customer.}
\displaystyle \text{(ii) The final price paid for the coloured T.V.}
\displaystyle \text{Answer:}
\displaystyle \text{Catalog price of the coloured T.V.}=\text{Rs. }18000
\displaystyle \text{Price after }20\%\text{ discount}=\frac{80}{100}\times18000=\text{Rs. }14400
\displaystyle \text{Price after further }10\%\text{ discount}=\frac{90}{100}\times14400=\text{Rs. }12960
\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }12960=\frac{10}{100}\times12960=\text{Rs. }1296
\displaystyle \therefore \text{Sales Tax paid by the customer}=\text{Rs. }1296
\displaystyle \text{Final price paid}=12960+1296=\text{Rs. }14256
\\

\displaystyle \textbf{Question 6: } \text{A shopkeeper buys an article for Rs. }7500\text{ and increases its}
\displaystyle \text{price. He sells it for Rs. }9156\text{ including }9\%\text{ Sales Tax on the}
\displaystyle \text{increased price. Calculate by what percent he increases the price.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the increased price of the article}=\text{Rs. }x
\displaystyle x+\frac{9}{100}x=9156
\displaystyle \frac{109x}{100}=9156
\displaystyle x=\frac{9156\times100}{109}=\text{Rs. }8400
\displaystyle \text{Increase in price}=8400-7500=\text{Rs. }900
\displaystyle \text{Percentage increase}=\frac{900}{7500}\times100=12\%
\\

\displaystyle \textbf{Question 7: } \text{An article is marked at Rs. }500.\text{ The wholesaler sells it}
\displaystyle \text{to a retailer at a }20\%\text{ discount and charges Sales Tax at }12.5\%
\displaystyle \text{on the remaining price. The retailer sells it to a customer at its marked}
\displaystyle \text{price and charges Sales Tax at the same rate. Calculate:}
\displaystyle \text{(i) The price paid by the customer.}
\displaystyle \text{(ii) The amount of VAT paid by the retailer.}
\displaystyle \text{Answer:}
\displaystyle \text{Marked price of the article}=\text{Rs. }500
\displaystyle \text{Price paid by the retailer before Sales Tax}=\frac{80}{100}\times500=\text{Rs. }400
\displaystyle \text{Input VAT}=12.5\%\text{ of Rs. }400=\frac{12.5}{100}\times400=\text{Rs. }50
\displaystyle \text{Price paid by the retailer}=400+50=\text{Rs. }450
\displaystyle \text{Selling price to the customer before Sales Tax}=\text{Rs. }500
\displaystyle \text{Output VAT}=12.5\%\text{ of Rs. }500=\frac{12.5}{100}\times500=\text{Rs. }62.50
\displaystyle \therefore \text{Price paid by the customer}=500+62.50=\text{Rs. }562.50
\displaystyle \text{VAT paid by the retailer}=62.50-50=\text{Rs. }12.50
\\

\displaystyle \textbf{Question 8: } \text{An article is marked at Rs. }4500\text{ and the rate of Sales Tax}
\displaystyle \text{on it is }6\%.\text{ A trader buys it at some discount and sells it at the}
\displaystyle \text{marked price. If the trader pays Rs. }81\text{ as VAT, find:}
\displaystyle \text{(i) The percent discount received by the trader.}
\displaystyle \text{(ii) The total money paid by the trader, including tax, to buy the article.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the discount received by the trader}=x\%
\displaystyle \text{Cost price before tax}=4500\left(1-\frac{x}{100}\right)
\displaystyle \text{Input VAT}=6\%\text{ of }4500\left(1-\frac{x}{100}\right)
\displaystyle =\frac{6}{100}\times4500\left(1-\frac{x}{100}\right)
\displaystyle \text{Selling price before tax}=\text{Rs. }4500
\displaystyle \text{Output VAT}=6\%\text{ of Rs. }4500=\frac{6}{100}\times4500=\text{Rs. }270
\displaystyle \text{VAT payable}=81
\displaystyle 270-\frac{6}{100}\times4500\left(1-\frac{x}{100}\right)=81
\displaystyle 270-270\left(1-\frac{x}{100}\right)=81
\displaystyle 270\left(\frac{x}{100}\right)=81
\displaystyle x=\frac{81\times100}{270}=30
\displaystyle \therefore \text{Discount received by the trader}=30\%
\displaystyle \text{Cost price before tax}=4500\left(1-\frac{30}{100}\right)=\text{Rs. }3150
\displaystyle \text{Tax paid by the trader}=6\%\text{ of Rs. }3150=\text{Rs. }189
\displaystyle \therefore \text{Total money paid by the trader}=3150+189=\text{Rs. }3339
\\

\displaystyle \textbf{Question 9: } \text{A retailer sells an article for Rs. }5350\text{ including }7\%
\displaystyle \text{Sales Tax on the listed price. If he bought it at a discount and made}
\displaystyle \text{a profit of }25\%\text{ on the whole, find the rate of discount he gets.}
\displaystyle \text{Answer:}
\displaystyle \text{Let the list price of the article}=\text{Rs. }x
\displaystyle x+\frac{7}{100}x=5350
\displaystyle \frac{107x}{100}=5350
\displaystyle x=\frac{5350\times100}{107}=\text{Rs. }5000
\displaystyle \text{Selling price before Sales Tax}=\text{Rs. }5000
\displaystyle \text{Since profit is }25\%,\text{ cost price}=\frac{100}{125}\times5000=\text{Rs. }4000
\displaystyle \text{Discount}=5000-4000=\text{Rs. }1000
\displaystyle \text{Rate of discount}=\frac{1000}{5000}\times100=20\%
\\

\displaystyle \textbf{Question 10: } \text{The printed price of an article is Rs. }9600.\text{ A shopkeeper buys}
\displaystyle \text{it at a discount of }20\%\text{ and sells it at the printed price. If the}
\displaystyle \text{rate of Sales Tax is }10\%,\text{ find:}
\displaystyle \text{(i) The VAT paid by the shopkeeper.}
\displaystyle \text{(ii) The profit made by the shopkeeper if he spends Rs. }120\text{ on}
\displaystyle \text{transportation of the article.}
\displaystyle \text{Answer:}
\displaystyle \text{Printed price of the article}=\text{Rs. }9600
\displaystyle \text{Cost price after }20\%\text{ discount}=\frac{80}{100}\times9600=\text{Rs. }7680
\displaystyle \text{Input VAT}=10\%\text{ of Rs. }7680=\text{Rs. }768
\displaystyle \text{Selling price before Sales Tax}=\text{Rs. }9600
\displaystyle \text{Output VAT}=10\%\text{ of Rs. }9600=\text{Rs. }960
\displaystyle \therefore \text{VAT paid by the shopkeeper}=960-768=\text{Rs. }192
\displaystyle \text{Total cost price}=7680+120=\text{Rs. }7800
\displaystyle \text{Profit}=9600-7800=\text{Rs. }1800
\\

\displaystyle \textbf{Question 11: } \text{A shopkeeper buys a camera at a discount of }20\%\text{ from the}
\displaystyle \text{wholesaler. The printed price of the camera is Rs. }1600\text{ and the rate}
\displaystyle \text{of Sales Tax is }6\%.\text{ He sells it at the printed price and charges}
\displaystyle \text{Sales Tax at the same rate. Find:}\hfill \text{[ICSE 2008]}
\displaystyle \text{(i) The price at which the camera can be bought from the shopkeeper.}
\displaystyle \text{(ii) The VAT paid by the shopkeeper.}
\displaystyle \text{Answer:}
\displaystyle \text{Printed price of the camera}=\text{Rs. }1600
\displaystyle \text{Cost price after }20\%\text{ discount}=\frac{80}{100}\times1600=\text{Rs. }1280
\displaystyle \text{Input VAT}=6\%\text{ of Rs. }1280=\text{Rs. }76.80
\displaystyle \text{Selling price before Sales Tax}=\text{Rs. }1600
\displaystyle \text{Output VAT}=6\%\text{ of Rs. }1600=\text{Rs. }96
\displaystyle \therefore \text{Price paid by the customer}=1600+96=\text{Rs. }1696
\displaystyle \therefore \text{VAT paid by the shopkeeper}=96-76.80=\text{Rs. }19.20
\\

\displaystyle \textbf{Question 12: } \text{A person bought an article for Rs. }8000\text{ and spent Rs. }1000
\displaystyle \text{on transportation. He marked it at Rs. }11700\text{ and sold it to a}
\displaystyle \text{customer. If the customer had to pay }10\%\text{ Sales Tax, find:}\hfill \text{[ICSE 2010]}
\displaystyle \text{(i) The customer's price.}\qquad\text{(ii) His profit percent.}
\displaystyle \text{Answer:}
\displaystyle \text{Cost price of the article}=\text{Rs. }8000
\displaystyle \text{Transportation charges}=\text{Rs. }1000
\displaystyle \therefore \text{Total cost price}=8000+1000=\text{Rs. }9000
\displaystyle \text{Marked price}=\text{Rs. }11700
\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }11700=\frac{10}{100}\times11700=\text{Rs. }1170
\displaystyle \therefore \text{Customer's price}=11700+1170=\text{Rs. }12870
\displaystyle \text{Profit}=11700-9000=\text{Rs. }2700
\displaystyle \text{Profit }\%=\frac{2700}{9000}\times100=30\%
\\

\displaystyle \textbf{Question 13: } \text{A shopkeeper sells an article at the listed price of Rs. }1500
\displaystyle \text{and the rate of VAT is }12\%\text{ at each stage of sale. If he pays}
\displaystyle \text{VAT of Rs. }36\text{ to the Government, find the price, inclusive of tax,}
\displaystyle \text{at which he purchased it from the wholesaler.}\hfill \text{[ICSE 2013]}
\displaystyle \text{Answer:}
\displaystyle \text{Listed price of the article}=\text{Rs. }1500
\displaystyle \text{Output VAT}=12\%\text{ of Rs. }1500=\frac{12}{100}\times1500=\text{Rs. }180
\displaystyle \text{Let the purchase price before tax}=\text{Rs. }x
\displaystyle \text{Input VAT}=12\%\text{ of Rs. }x=\frac{12}{100}x
\displaystyle \text{VAT payable}=180-\frac{12}{100}x=36
\displaystyle \frac{12}{100}x=144
\displaystyle x=\frac{144\times100}{12}=\text{Rs. }1200
\displaystyle \text{Sales Tax paid by the shopkeeper}=12\%\text{ of Rs. }1200=\text{Rs. }144
\displaystyle \therefore \text{Price paid by the shopkeeper}=1200+144=\text{Rs. }1344
\\

\displaystyle \textbf{Question 14: } \text{A shopkeeper bought a washing machine at a discount of }20\%
\displaystyle \text{from a wholesaler, the printed price being Rs. }18000.\text{ He sells it}
\displaystyle \text{to a consumer at a discount of }10\%\text{ on the printed price. If the rate}
\displaystyle \text{of Sales Tax is }8\%,\text{ find:}\hfill \text{[ICSE 2014]}
\displaystyle \text{(i) The VAT paid by the shopkeeper.}
\displaystyle \text{(ii) The total amount paid by the consumer.}
\displaystyle \text{Answer:}
\displaystyle \text{Printed price of the washing machine}=\text{Rs. }18000
\displaystyle \text{Cost price after }20\%\text{ discount}=\frac{80}{100}\times18000=\text{Rs. }14400
\displaystyle \text{Input VAT}=8\%\text{ of Rs. }14400=\frac{8}{100}\times14400=\text{Rs. }1152
\displaystyle \text{Selling price after }10\%\text{ discount}=\frac{90}{100}\times18000=\text{Rs. }16200
\displaystyle \text{Output VAT}=8\%\text{ of Rs. }16200=\frac{8}{100}\times16200=\text{Rs. }1296
\displaystyle \therefore \text{VAT paid by the shopkeeper}=1296-1152=\text{Rs. }144
\displaystyle \therefore \text{Total amount paid by the consumer}=16200+1296=\text{Rs. }17496
\\

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