Class 10: Sales Tax and VAT

$\displaystyle \textbf{Question 1: } \text{A person buys an unfinished article for Rs. }1800\text{ and spends}$
$\displaystyle \text{Rs. }600\text{ on its finishing, packing, transportation, etc. He marks}$
$\displaystyle \text{the article at such a price that gives him }20\%\text{ profit. How much}$
$\displaystyle \text{will a customer pay including }12\%\text{ Sales Tax?}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Cost of unfinished article}=\text{Rs. }1800$
$\displaystyle \text{Overheads}=\text{Rs. }600$
$\displaystyle \therefore \text{Total cost price}=1800+600=\text{Rs. }2400$
$\displaystyle \text{Desired profit}=20\%$
$\displaystyle \text{Selling price}=\frac{120}{100}\times2400=\text{Rs. }2880$
$\displaystyle \text{Sales Tax}=12\%\text{ of Rs. }2880=\frac{12}{100}\times2880=\text{Rs. }345.60$
$\displaystyle \therefore \text{Amount paid by the customer}=2880+345.60=\text{Rs. }3225.60$
$\\$

$\displaystyle \textbf{Question 2: } \text{A person buys an article for Rs. }800\text{ and spends Rs. }100$
$\displaystyle \text{on its transportation, etc. He marks the article at a certain price and}$
$\displaystyle \text{sells it for Rs. }1287\text{ including }10\%\text{ Sales Tax. Find his}$
$\displaystyle \text{profit as a percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Cost of the article}=\text{Rs. }800$
$\displaystyle \text{Overheads}=\text{Rs. }100$
$\displaystyle \therefore \text{Total cost price}=800+100=\text{Rs. }900$
$\displaystyle \text{Let the selling price (before Sales Tax)}=\text{Rs. }x$
$\displaystyle x+\frac{10}{100}x=1287$
$\displaystyle \frac{110x}{100}=1287$
$\displaystyle x=\frac{1287\times100}{110}=\text{Rs. }1170$
$\displaystyle \text{Profit}=1170-900=\text{Rs. }270$
$\displaystyle \therefore \text{Profit }\%=\frac{270}{900}\times100=30\%$
$\\$

$\displaystyle \textbf{Question 3: } \text{A person announces a discount of }15\%\text{ on his goods. If the}$
$\displaystyle \text{marked price of an article is Rs. }6000,\text{ how much does a customer}$
$\displaystyle \text{have to pay if the rate of Sales Tax is }10\%?$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Marked price of the article}=\text{Rs. }6000$
$\displaystyle \text{Discount}=15\%\text{ of the marked price}$
$\displaystyle \text{Discounted price}=\frac{100-15}{100}\times6000=\text{Rs. }5100$
$\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }5100=\frac{10}{100}\times5100=\text{Rs. }510$
$\displaystyle \therefore \text{Amount paid by the customer}=5100+510=\text{Rs. }5610$
$\\$

$\displaystyle \textbf{Question 4: } \text{The catalog price of a coloured T.V. is Rs. }24000.$
$\displaystyle \text{The shopkeeper gives a discount of }8\%\text{ on the list price. He gives}$
$\displaystyle \text{a further off-season discount of }5\%\text{ on the balance. Sales Tax at}$
$\displaystyle \text{10\% is charged on the remaining amount. Find:}\hfill \text{[ICSE 2001]}$
$\displaystyle \text{(i) The Sales Tax paid by the customer.}$
$\displaystyle \text{(ii) The final price paid for the T.V.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Catalog price of the coloured T.V.}=\text{Rs. }24000$
$\displaystyle \text{Price after }8\%\text{ discount}=\frac{92}{100}\times24000=\text{Rs. }22080$
$\displaystyle \text{Price after further }5\%\text{ discount}=\frac{95}{100}\times22080=\text{Rs. }20976$
$\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }20976=\frac{10}{100}\times20976=\text{Rs. }2097.60$
$\displaystyle \therefore \text{Sales Tax paid by the customer}=\text{Rs. }2097.60$
$\displaystyle \text{Final price paid}=20976+2097.60=\text{Rs. }23073.60$
$\\$

$\displaystyle \textbf{Question 5: } \text{A person marks his goods }40\%\text{ above the cost price and then}$
$\displaystyle \text{allows a discount of }20\%.\text{ Find how much a customer will pay for}$
$\displaystyle \text{an article that costs the person Rs. }200\text{ and Sales Tax of }10\%$
$\displaystyle \text{is levied on the sales price of the article.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Cost price of the article}=\text{Rs. }200$
$\displaystyle \text{Marked price}=200+40\%\text{ of Rs. }200$
$\displaystyle =200+\frac{40}{100}\times200=\text{Rs. }280$
$\displaystyle \text{Discount}=20\%\text{ of marked price}$
$\displaystyle \text{Selling price}=\frac{100-20}{100}\times280=\text{Rs. }224$
$\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }224=\frac{10}{100}\times224=\text{Rs. }22.40$
$\displaystyle \therefore \text{Amount paid by the customer}=224+22.40=\text{Rs. }246.40$
$\\$

$\displaystyle \textbf{Question 6: } \text{A toy is purchased for Rs. }591.36\text{ which includes }12\%$
$\displaystyle \text{rebate on the printed price and }12\%\text{ Sales Tax on the sales price}$
$\displaystyle \text{of the toy. Find the printed price of the toy.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the printed price of the toy}=\text{Rs. }x$
$\displaystyle \text{Rebate}=12\%$
$\displaystyle \text{Selling price after rebate}=\frac{100-12}{100}x=\frac{88x}{100}$
$\displaystyle \text{Sales Tax}=12\%\text{ of }\frac{88x}{100}=\frac{12}{100}\times\frac{88x}{100}$
$\displaystyle \text{Amount paid}=\frac{88x}{100}+\frac{12}{100}\times\frac{88x}{100}$
$\displaystyle =\frac{88x}{100}\times\frac{112}{100}=\frac{9856x}{10000}$
$\displaystyle \therefore \frac{9856x}{10000}=591.36$
$\displaystyle x=\frac{591.36\times10000}{9856}=\text{Rs. }600$
$\displaystyle \therefore \text{Printed price of the toy}=\text{Rs. }600$
$\\$

$\displaystyle \textbf{Question 7: } \text{The catalog price of an article is Rs. }20000.\text{ The person allows}$
$\displaystyle \text{two successive discounts of }15\%\text{ and }10\%.\text{ If Sales Tax at the rate}$
$\displaystyle \text{of }10\%\text{ is charged on the remaining amount, find:}$
$\displaystyle \text{(i) The Sales Tax amount a customer has to pay.}$
$\displaystyle \text{(ii) The final total price that the customer has to pay.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Catalog price of the article}=\text{Rs. }20000$
$\displaystyle \text{Price after }15\%\text{ discount}=\frac{85}{100}\times20000=\text{Rs. }17000$
$\displaystyle \text{Price after further }10\%\text{ discount}=\frac{90}{100}\times17000=\text{Rs. }15300$
$\displaystyle \text{Sales Tax}=10\%\text{ of Rs. }15300=\frac{10}{100}\times15300=\text{Rs. }1530$
$\displaystyle \therefore \text{Sales Tax paid by the customer}=\text{Rs. }1530$
$\displaystyle \text{Final price paid}=15300+1530=\text{Rs. }16830$
$\\$

$\displaystyle \textbf{Question 8: } \text{A person buys an article for Rs. }1700\text{ at a discount of}$
$\displaystyle 15\%\text{ on its printed price. He raises the printed price of the article}$
$\displaystyle \text{by }20\%\text{ and then sells it for Rs. }2688\text{ including Sales Tax on the}$
$\displaystyle \text{new marked price. Find:}$
$\displaystyle \text{(i) The rate of Sales Tax.}$
$\displaystyle \text{(ii) The trader's profit as a percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the original printed price of the article}=\text{Rs. }x$
$\displaystyle \text{Cost price of the article for the trader}=\frac{85}{100}x$
$\displaystyle \therefore \frac{85}{100}x=1700$
$\displaystyle x=\frac{1700\times100}{85}=\text{Rs. }2000$
$\displaystyle \text{New marked price}=2000+\frac{20}{100}\times2000=\text{Rs. }2400$
$\displaystyle \text{Let the rate of Sales Tax}=r\%$
$\displaystyle 2400+\frac{r}{100}\times2400=2688$
$\displaystyle 2400\left(1+\frac{r}{100}\right)=2688$
$\displaystyle 1+\frac{r}{100}=\frac{2688}{2400}=1.12$
$\displaystyle \frac{r}{100}=0.12$
$\displaystyle r=12$
$\displaystyle \therefore \text{Rate of Sales Tax}=12\%$
$\displaystyle \text{Profit}=2400-1700=\text{Rs. }700$
$\displaystyle \text{Profit }\%=\frac{700}{1700}\times100=41\frac{3}{17}\%$
$\\$

$\displaystyle \textbf{Question 9: } \text{A person buys an article at a rebate of }20\%\text{ on its marked price}$
$\displaystyle \text{and then spends Rs. }300\text{ on transportation, etc. If he sells the article}$
$\displaystyle \text{for Rs. }4160\text{ including Sales Tax at }4\%\text{ of the marked price, find}$
$\displaystyle \text{the person's profit as a percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the marked price of the article}=\text{Rs. }x$
$\displaystyle \text{Cost price after }20\%\text{ rebate}=\frac{80}{100}x=\text{Rs. }0.8x$
$\displaystyle \text{Overheads}=\text{Rs. }300$
$\displaystyle \text{Sales Tax}=4\%\text{ of Rs. }x=\frac{4}{100}x=\text{Rs. }0.04x$
$\displaystyle \text{Amount paid by the customer}=x+0.04x=4160$
$\displaystyle 1.04x=4160$
$\displaystyle x=\frac{4160}{1.04}=\text{Rs. }4000$
$\displaystyle \text{Total cost price}=0.8\times4000+300=\text{Rs. }3500$
$\displaystyle \text{Selling price excluding Sales Tax}=\text{Rs. }4000$
$\displaystyle \text{Profit}=4000-3500=\text{Rs. }500$
$\displaystyle \text{Profit }\%=\frac{500}{3500}\times100=14\frac{2}{7}\%$
$\\$

$\displaystyle \textbf{Question 10: } \text{A person buys an article for Rs. }2400\text{ from a wholesaler}$
$\displaystyle \text{at }20\%\text{ rebate on its list price. He marks up the list price by}$
$\displaystyle 10\%\text{ and then sells it for Rs. }3498\text{ including Sales Tax on the}$
$\displaystyle \text{marked-up price. Find:}$
$\displaystyle \text{(i) The rate of Sales Tax.}$
$\displaystyle \text{(ii) The person's profit as a percent.}$
$\displaystyle \text{Answer:}$
$\displaystyle \text{Let the list price of the article}=\text{Rs. }x$
$\displaystyle \text{Cost price after }20\%\text{ rebate}=\frac{80}{100}x$
$\displaystyle \frac{80}{100}x=2400$
$\displaystyle x=\frac{2400\times100}{80}=\text{Rs. }3000$
$\displaystyle \text{New marked price}=3000+\frac{10}{100}\times3000=\text{Rs. }3300$
$\displaystyle \text{Let the rate of Sales Tax}=r\%$
$\displaystyle 3300+\frac{r}{100}\times3300=3498$
$\displaystyle 3300\left(1+\frac{r}{100}\right)=3498$
$\displaystyle 1+\frac{r}{100}=\frac{3498}{3300}=1.06$
$\displaystyle \frac{r}{100}=0.06$
$\displaystyle r=6$
$\displaystyle \therefore \text{Rate of Sales Tax}=6\%$
$\displaystyle \text{Profit}=3300-2400=\text{Rs. }900$
$\displaystyle \text{Profit }\%=\frac{900}{2400}\times100=37.5\%$
$\\$