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

Question 1: A person purchases a compact computer system for Rs.47700 which includes 10% rebate on the marked price and then 6% Sales Tax on the remaining price. Find the marked price of the computer.

Let the marked price $= x$

Sale price $=$ $\frac{100-10}{100}$ $\times x +$ $\frac{6}{100}$ $\times \Big($ $\frac{100-10}{100}$ $\times x \Big)$

Given $47700 =$ $\frac{100-10}{100}$ $\times x +$ $\frac{6}{100}$ $\times \Big($ $\frac{100-10}{100}$ $\times x \Big)$

$\Rightarrow x = Rs. \ 50000$

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Question 2: A wholesaler sells an article for Rs.2700 at a discount of 10% on the printed price to a retailer. The retailer, in turn, raises the printed price of the article by 15% and sells it for Rs.3657 which includes Sales Tax on the new market price. Find:

The rate of Sales Tax

The Profit, as per cent, made by the retailer

Let the printed price of the article is $Rs. \ x$

Therefore $x \Big(1-$ $\frac{10}{100}$ $\Big) = 2700 \Rightarrow x = Rs. \ 3000$

Let the Sales Tax rate $= r\%$

$3000 \Big(1+$ $\frac{15}{100}$ $\Big) \Big(1+$ $\frac{r}{100}$ $\Big)=3657 \Rightarrow r = 6\%$

Profit percentage made by the retailer $=$ $\frac{3450-2700}{2700}$ $= 27.78\%$

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Question 3: A shopkeeper buys an article at 70% of its printed price. He spends Rs.40 on transportation of the article. After charging Sales Tax at the rate of 10% on the printed price, he sells the article for Rs.7040. Find his profit as per cent to the nearest integer.

Let the printed price $= Rs. \ x$

Cost to the shopkeeper $= 0.7 \times x + 40$

Selling price (including the sales tax) $= Rs. \ 7040$

Therefore $x \Big(1+$ $\frac{10}{100}$ $\Big)= 7040 \Rightarrow x = Rs. \ 6400$

Cost to the shopkeeper $= 0.7 \times 6400 + 40 = Rs. \ 4520$

Profit % $=$ $\frac{6400-4520}{4520}$ $= 41.59\%$

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Question 4: A person bought a washing machine marked at Rs.9375. The rate of Sales Tax is 6%. She asks the shopkeeper to reduce the price of the washing machine to such an extent that she has to pay Rs.9275 inclusive of Sales Tax. Find the reduction needed in the price of the washing machine.

Let the cost price after reduction $= Rs. \ x$

Therefore $x \Big(1+$ $\frac{6}{100}$ $\Big) = 9275 \Rightarrow x = Rs. \ 8750$

Reduction needed $= 9375-8750 = Rs. 625$

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Question 5: The catalog price of a colored T.V. is Rs.18000. The shopkeeper sells it to a customer at a discount of 20% on the catalog price. He gives a further off-season discount of 10% on the balance. Sales Tax at 10% is charged on the remaining amount. Find:

The Sales Tax amount, the customer has to pay.

The final price he has to pay for the color T.V.

The catalog price of a colored T.V. is $Rs. \ 18000$

Catalog price for the customer $= 18000 \Big(1-$ $\frac{20}{100}$ $\Big) \Big(1-$ $\frac{10}{100}$ $\Big) = Rs. 12960$

Sales tax charged $= 12960 \times$ $\frac{10}{100}$ $= Rs. \ 1296$

Final price for the customer $= 12960+1296 = Rs. \ 14256$

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Question 6: A shopkeeper buys an article for Rs.7500 and increases its price. He sells this article for Rs.9156 including 9% Sales Tax on the increased price. Calculate, by how much per cent the shopkeeper increases the price of the article.

Let the increased price be $= Rs. \ x$

Therefore $x \Big(1+$ $\frac{9}{100}$ $\Big) = 9156 \Rightarrow x = Rs. \ 8400$

Percentage increase $=$ $\frac{8400-7500}{7500}$ $= 12\%$

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Question 7: An article is marked at Rs.500. The wholesaler sells it to a retailer at 20% discount and charges Sales-Tax on the remaining price at 12.5%. The retailer, in turn, sells the article to a customer at its marked price and charges Sales-Tax at the same rate. Calculate;

The price paid by the customer

The amount of VAT paid by the retailer

Marked Price $= Rs. \ 500$

Price Paid by the retailer $= 500 \Big(1-$ $\frac{20}{100}$ $\Big) \Big(1+$ $\frac{12.5}{100}$ $\Big) = Rs.\ 450$

Price paid by the customer $= 500 \Big(1+$ $\frac{12.5}{100}$ $\Big) = Rs. \ 562.5$

Vat paid by the retailer $= \Big(500-500 \Big(1-$ $\frac{20}{100}$ $\Big) \Big) \times$ $\frac{12.5}{100}$ $= Rs. \ 12.5$

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Question 8: An article is marked at Rs.4500 and the rate of Sales-Tax on it is 6%. A trader buys this article at some discount and sells it to a customer at the marked price. If the trader pays Rs.81 as VAT; Find:

How much per cent discount does the trader get?

The total money paid by the trader, including tax, to buy the article.

Let the discount be $= x\%$

Cost Price for the trader $= 4500 \Big(1-$ $\frac{x}{100}$ $\Big)$

Sales Tax Paid by the trader $= 4500 \Big(1-$ $\frac{x}{100}$ $\Big) \times$ $\frac{6}{100}$

Selling Price for the trader $= Rs. \ 4500$

Sales Tax on the sales $= 4500 \times$ $\frac{6}{100}$

Therefore

$4500 \times$ $\frac{6}{100}$ $-4500 \Big(1-$ $\frac{x}{100}$ $\Big) \times$ $\frac{6}{100}$ $= 81$

Solving for $x$ we get $x = 30\%$

Total cost of the trader $= 4500 \Big(1-$ $\frac{30}{100}$ $\Big) \times 1.06 = Rs. \ 3339$

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Question 9: A retailer sells an article for Rs.5350 including 7% Sales Tax on the listed price. If he has bought it at a discount and has made a profit of 25% on the whole, find the rate of discount he gets.

Let the list price$= Rs. \ x$

Therefore$x+x \times$ $\frac{7}{100}$ $= 5350 \Rightarrow x = Rs. \ 5000$

Let the discount %$= d\%$

Therefore

$\frac{5000-5000(1-\frac{d}{100})}{5000(1-\frac{d}{100})}$ $=$ $\frac{25}{100}$

$\Rightarrow d = 20\%$

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Question 10: The printed price of an article is Rs.9600. A shopkeeper buys it at a discount of 20% and sells it at the printed price. Find the amount of VAT paid by the shopkeeper, if the rate of Sales Tax is 10%. Also, Find the profit made by the shopkeeper, if he spends Rs.120 on the transportation of the article.

Listed Price   $= Rs. \ 9600$

Discount  $= 20\%$

Cost Price  $= 9600 \times 0.8 = Rs. 7680$

Selling Price  $= Rs. 9600$

Sales Tax rate  $= 10\%$

Sales Tax paid by the shopkeeper  $= 7680 \times$ $\frac{10}{100}$ $= Rs. \ 768$

Sales Tax paid by the customer  $= 9600 \times$ $\frac{10}{100}$ $= Rs. \ 960$

VAT  $= 960-768 = Rs. \ 192$

Profit  $= 9600-7680-120 = Rs. \ 1800$

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Question 11: A shopkeeper buys a camera at a discount of 20% from the wholesaler, the printed price of the camera being Rs.1600 and the rate of sales tax is 6%. The shopkeeper sells it to the buyer at the printed price and charges tax at the same rate. Find:

The price at which the camera can be bought from the shopkeeper.

The VAT paid by the shopkeeper [2008]

Printed Price of the camera   $= Rs. \ 1600$

Discount  $= 20\%$

Sales Tax  $= 6\%$

Cost Price of the shopkeeper  $= 1600 \times 0.8 = Rs.\ 1280$

Sales Tax on Cost Price  $= 1280 \times$ $\frac{6}{100}$ $= Rs.\ 76.80$

Sale Price  $= Rs. 1600$

Price the the customer have to pay  $= 1600+1600 \times$ $\frac{6}{100}$ $= Rs.\ 1696$

Sales Tax paid by the customer  $= 1600 \times$ $\frac{6}{100}$ $= Rs.\ 96$

VAT  $= 96-76.80 = Rs.\ 19.2$

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Question 12: A person bought an article for Rs.8000 and spent Rs.1000 for transportation. He marked the article at Rs.11700 and sold it to a customer. If the customer had to pay 10% sales tax, Find:

The customer’s Price

His’s Profit percent [2010]

Cost Price  $= Rs. 8000$

Overheads $= Rs. 1000$

Listed Price $= Rs. 11700$

Sales Tax rate $= 10\%$

Customer Price $= 11700+11700 \times$ $\frac{10}{100}$ $= Rs. 12870$

Profit $=$ $\frac{11700-8000-1000}{9000}$ $= 30\%$

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Question 13: A Shopkeeper sells an article at the listed price of Rs.1500 and the rate of VAT is 12% at each stage of sale. If the shopkeeper pays a VAT of Rs.36 to the Government, what was the price, inclusive of Tax, at which the shopkeeper purchased the article from the wholesaler? [2013]

Listed price  $= Rs. \ 1500$

Sales Tax paid by the shopkeeper $= 1500 \times$ $\frac{12}{100}$ $= Rs. \ 180$

Let the price at which the shopkeeper purchased the article $= Rs. \ x$

Therefore

$180 - x \times$ $\frac{12}{100}$ $= 36 \Rightarrow x = Rs. 1200$

Sales tax paid $= 1200 \times$ $\frac{12}{100}$ $= Rs. \ 144$

Total price paid by the shopkeeper $= 1200+144 = Rs. 1344$

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Question 14: A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs.18000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:

The VAT paid by the shopkeeper

The total amount that the consumer pays for the washing machine. [2014]

Printed Price  $= Rs. \ 18000$

Discount $=20\%$

Cost Price for the shopkeeper $= 18000 \times 0.80 = Rs. \ 14400$

Sales Tax paid by the shopkeeper $= 14400 \times$ $\frac{8}{100}$ $= Rs. \ 1152$

Selling price to the customer  $= 18000 \times 0.90 = Rs. \ 16200$

Sales tax paid by the customer $= 16200 \times$ $\frac{8}{100}$ $= Rs. \ 1296$

VAT paid by the shopkeeper $= 1295 - 1152 = Rs. \ 144$

The total amount paid by the customer $= 16200+1296 = Rs. \ 17496$

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