\displaystyle \textbf{Question 1. }\text{The price of a T.V. inclusive of }9\%\text{ Sales Tax is Rs. }13407. \\ \text{Find the marked price and the extra amount payable if the tax becomes }13\%.\text{ [ICSE Board 2002]}
\displaystyle \text{Answer:}
\displaystyle \text{Let the marked price be Rs. }P.
\displaystyle P+\frac{9}{100}P=13407
\displaystyle \frac{109P}{100}=13407
\displaystyle P=\frac{13407\times100}{109}=\text{Rs. }12300
\displaystyle \text{Extra amount payable}=\frac{13-9}{100}\times12300
\displaystyle =\frac{4}{100}\times12300=\text{Rs. }492
\displaystyle \text{Hence, the marked price is Rs. }12300\text{ and the extra amount payable is Rs. }492.
\\

\displaystyle \textbf{Question 2. }\text{The price of a washing machine inclusive of }10\%\text{ Sales Tax is} \\ \text{Rs. }13530.\text{ Find its basic price. [ICSE Board 2003]}
\displaystyle \text{Answer:}
\displaystyle \text{Let the basic price be Rs. }P.
\displaystyle P+\frac{10}{100}P=13530
\displaystyle \frac{110P}{100}=13530
\displaystyle P=\frac{13530\times100}{110}=\text{Rs. }12300
\displaystyle \text{Hence, the basic price of the washing machine is Rs. }12300.
\\

\displaystyle \textbf{Question 3. }\text{A T.V. is marked at Rs. }24000.\text{ Successive discounts of }8\% \\ \text{ and }5\%\text{ are allowed, followed by }10\%\text{ sales tax. Find the tax and the} \\ \text{final price. [ICSE Board 2001]}
\displaystyle \text{Answer:}
\displaystyle \text{Marked Price}=\text{Rs. }24000
\displaystyle \text{Price after }8\%\text{ discount}=24000\left(1-\frac{8}{100}\right)=\text{Rs. }22080
\displaystyle \text{Price after }5\%\text{ discount}=22080\left(1-\frac{5}{100}\right)=\text{Rs. }20976
\displaystyle \text{Sales Tax}=10\%\text{ of }20976=\text{Rs. }2097.60
\displaystyle \text{Final Price}=20976+2097.60=\text{Rs. }23073.60
\displaystyle \text{Hence, the sales tax is Rs. }2097.60\text{ and the final price is Rs. }23073.60.
\\

\displaystyle \textbf{Question 4. }\text{The marked price of an article is Rs. }5000.\text{ A wholesaler allows a} \\ \text{discount of }25\%\text{ and a retailer allows a discount of }15\%.\text{ VAT is }8\%.\text{ Find the} \\ \text{VAT payable by the wholesaler and the retailer. [ICSE Board 2010]}
\displaystyle \text{Answer:}
\displaystyle \text{Wholesaler's selling price}=5000\left(1-\frac{25}{100}\right)=\text{Rs. }3750
\displaystyle \text{Output VAT collected by wholesaler}=8\%\text{ of }3750=\text{Rs. }300
\displaystyle \text{Retailer's cost price including VAT}=3750+300=\text{Rs. }4050
\displaystyle \text{Retailer's selling price before VAT}=5000\left(1-\frac{15}{100}\right)=\text{Rs. }4250
\displaystyle \text{Output VAT collected by retailer}=8\%\text{ of }4250=\text{Rs. }340
\displaystyle \text{VAT payable by retailer}=340-300=\text{Rs. }40
\displaystyle \text{If the customer pays Rs. }5000,\text{ then VAT charged to the customer}=8\%\text{ of }5000=\text{Rs. }400
\displaystyle \text{VAT payable by wholesaler}=300-260=\text{Rs. }40
\displaystyle \text{Hence, the VAT payable by the wholesaler is Rs. }40\text{ and by the retailer is Rs. }40.
\\

\displaystyle \textbf{Question 5. }\text{A computer is marked at Rs. }45000.\text{ Successive discounts of }7\% \\ \text{ and }4\%\text{ are allowed, followed by }8\%\text{ sales tax. Find the tax and the final} \\ \text{price. [ICSE Board 2005]}
\displaystyle \text{Answer:}
\displaystyle \text{Marked Price}=\text{Rs. }45000
\displaystyle \text{Price after }7\%\text{ discount}=45000\left(1-\frac{7}{100}\right)=\text{Rs. }41850
\displaystyle \text{Price after }4\%\text{ discount}=41850\left(1-\frac{4}{100}\right)=\text{Rs. }40176
\displaystyle \text{Sales Tax}=8\%\text{ of }40176=\text{Rs. }3214.08
\displaystyle \text{Final Price}=40176+3214.08=\text{Rs. }43390.08
\displaystyle \text{Hence, the sales tax is Rs. }3214.08\text{ and the final price is Rs. }43390.08.
\\

\displaystyle \textbf{Question 6. }\text{An article is sold for Rs. }374\text{ after allowing a discount of }15\% \\ \text{ and charging }10\%\text{ sales tax. Find the marked price. [ICSE Board 2007]}
\displaystyle \text{Answer:}
\displaystyle \text{Let the marked price be Rs. }P.
\displaystyle \text{Price after }15\%\text{ discount}=0.85P
\displaystyle \text{Price after adding }10\%\text{ sales tax}=1.10\times0.85P=374
\displaystyle 0.935P=374
\displaystyle P=\frac{374}{0.935}=\text{Rs. }400
\displaystyle \text{Hence, the marked price of the article is Rs. }400.
\\

\displaystyle \textbf{Question 7. }\text{Manufacturer }\rightarrow\text{ Wholesaler }\rightarrow\text{ Trader.} \\ \text{VAT is }8\%.\text{ Find the government VAT and consumer price. [ICSE Board 2011]}
\displaystyle \text{Answer:}
\displaystyle \text{VAT paid by manufacturer}=\text{Rs. }1200
\displaystyle \text{VAT collected by wholesaler}=8\%\text{ of }16200=\text{Rs. }1296
\displaystyle \text{VAT paid by wholesaler}=1296-1200=\text{Rs. }96
\displaystyle \text{VAT collected by trader}=8\%\text{ of }18000=\text{Rs. }1440
\displaystyle \text{VAT paid by trader}=1440-1296=\text{Rs. }144
\displaystyle \text{Total VAT received by government}=1200+96+144=\text{Rs. }1440
\displaystyle \text{Consumer price}=18000+1440=\text{Rs. }19440
\displaystyle \text{Hence, the government VAT is Rs. }1440\text{ and the consumer price is Rs. }19440.
\\

\displaystyle \textbf{Question 8. }\text{Printed price is Rs. }60000.\text{ Discount is }20\%\text{ and tax is } \\ 6\%.\text{ Find costs and VAT. [ICSE Board 2012]}
\displaystyle \text{Answer:}
\displaystyle \text{Cost after }20\%\text{ discount}=60000\left(1-\frac{20}{100}\right)=\text{Rs. }48000
\displaystyle \text{VAT paid}=6\%\text{ of }48000=\text{Rs. }2880
\displaystyle \text{Cost price including VAT}=48000+2880=\text{Rs. }50880
\displaystyle \text{VAT charged to customer}=6\%\text{ of }60000=\text{Rs. }3600
\displaystyle \text{VAT payable}=3600-2880=\text{Rs. }720
\displaystyle \text{Customer price}=60000+3600=\text{Rs. }63600
\displaystyle \text{Hence, VAT payable is Rs. }720\text{ and the customer price is Rs. }63600.
\\

\displaystyle \textbf{Question 9. }\text{A camera is marked at Rs. }1600.\text{ A discount of }20\%\text{ is allowed} \\ \text{and VAT is charged at }6\%.\text{ Find the cost price, VAT and the price paid} \\ \text{by the customer. [ICSE Board 2008]}
\displaystyle \text{Answer:}
\displaystyle \text{Cost price after }20\%\text{ discount}=1600\left(1-\frac{20}{100}\right)=\text{Rs. }1280
\displaystyle \text{VAT paid by the dealer}=6\%\text{ of }1280=\text{Rs. }76.80
\displaystyle \text{Customer price}=1600+6\%\text{ of }1600
\displaystyle =1600+96=\text{Rs. }1696
\displaystyle \text{VAT collected from the customer}=\text{Rs. }96
\displaystyle \text{VAT payable}=96-76.80=\text{Rs. }19.20
\displaystyle \text{Hence, the customer price is Rs. }1696\text{ and the VAT payable is Rs. }19.20.
\\

\displaystyle \textbf{Question 10. }\text{An article is purchased for Rs. }8000\text{ and overhead expenses are} \\ \text{Rs. }1000.\text{ It is marked at Rs. }11700\text{ and VAT is charged at }10\%.\text{ Find the price} \\ \text{paid by the customer and the profit percentage. [ICSE Board 2010]}
\displaystyle \text{Answer:}
\displaystyle \text{Total cost price}=8000+1000=\text{Rs. }9000
\displaystyle \text{VAT}=10\%\text{ of }11700=\text{Rs. }1170
\displaystyle \text{Customer price}=11700+1170=\text{Rs. }12870
\displaystyle \text{Profit}=11700-9000=\text{Rs. }2700
\displaystyle \text{Profit }\%= \frac{2700}{9000}\times100=30\%
\displaystyle \text{Hence, the customer price is Rs. }12870\text{ and the profit percentage is }30\%.
\\

\displaystyle \textbf{Question 11. }\text{The listed price of an article is Rs. }1500.\text{ VAT is }12\%. \\ \text{If the VAT payable is Rs. }36,\text{ find the purchase price including tax. [ICSE Board 2013]}
\displaystyle \text{Answer:}
\displaystyle \text{VAT on listed price}=12\%\text{ of }1500=\text{Rs. }180
\displaystyle \text{Let the purchase price before VAT be Rs. }P.
\displaystyle 180-12\%\text{ of }P=36
\displaystyle 180-\frac{12P}{100}=36
\displaystyle \frac{12P}{100}=144
\displaystyle P=\text{Rs. }1200
\displaystyle \text{Purchase price including VAT}=1200+12\%\text{ of }1200
\displaystyle =1200+144=\text{Rs. }1344
\displaystyle \text{Hence, the purchase price including VAT is Rs. }1344.
\\

\displaystyle \textbf{Question 12. }\text{The printed price of an article is Rs. }18000.\text{ Discounts of } \\ 20\%\text{ and }10\%\text{ are allowed and VAT is }8\%.\text{ Find the VAT payable and the total price} \\ \text{paid by the customer. [ICSE Board 2014]}
\displaystyle \text{Answer:}
\displaystyle \text{Cost price after }20\%\text{ discount}=18000\left(1-\frac{20}{100}\right)=\text{Rs. }14400
\displaystyle \text{Input VAT}=8\%\text{ of }14400=\text{Rs. }1152
\displaystyle \text{Selling price after }10\%\text{ discount}=18000\left(1-\frac{10}{100}\right)=\text{Rs. }16200
\displaystyle \text{Output VAT}=8\%\text{ of }16200=\text{Rs. }1296
\displaystyle \text{VAT payable}=1296-1152=\text{Rs. }144
\displaystyle \text{Total price paid by the customer}=16200+1296=\text{Rs. }17496
\displaystyle \text{Hence, the VAT payable is Rs. }144\text{ and the total price paid by the customer is Rs. }17496.
\\

Discover more from ICSE / ISC / CBSE Mathematics Portal for K12 Students

Subscribe to get the latest posts sent to your email.