Class 10: Sales Tax and Value Added Tax – Miscellaneous Problems-Set 1 – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: A person purchased a pair of shoes costing Rs. 850. Calculate the total amount to be paid by him, if the rate of Sales Tax is 6%.

Answer:

$\displaystyle \text{Sale price of shoes = Rs. 850 }$

$\displaystyle \text{and, Sales Tax = 6\% of Rs. 850 = Rs. 51 }$

$\displaystyle \text{Therefore total amount to be paid by Rohit = 850+51 =Rs. 901 }$

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Question 2: Mr. Gupta purchased an article for Rs. 702 including Sales Tax. If the rate of Sales Tax is 8%, find the sale price of the article.

Answer:

$\displaystyle \text{Let the sale price of the article be Rs. } x$

$\displaystyle \text{Therefore } x + 8\% \text{ of } x = 702$

$\displaystyle \Rightarrow x = 702 \times \frac{100}{108} = 650$

$\displaystyle \text{Therefore the sale price of the article = Rs. } 650$

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Question 3: A person purchased a face-cream for Rs. 79.10 including Sales Tax. If the printed price of the face-cream is Rs. 70; find the rate of Sales Tax.

Answer:

$\displaystyle \text{Total price (including Sales Tax) = Rs. } 79.10$

$\displaystyle \text{Printed price = Rs. } 70$

$\displaystyle \text{Therefore Sales Tax Paid } = 79.10-70 = \text{ Rs. } 9.10$

$\displaystyle \text{and, the rate of Sales Tax } = \frac{9.10}{70} \times 100 = 13\%$

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Question 4: Mr. Sharma purchased confectionery goods costing Rs. 165 on which the rate of Sales Tax is 6% and some tooth-paste, shaving-cream, soap, etc., costing Rs. 230 on which the rate of Sales Tax is 10%. If she gives a five-hundred rupee note to the shopkeeper, what money will he return to Mrs. Sharma ?

Answer:

$\displaystyle \text{Price of confectionery goods including Sales Tax } = 165 + 6\% \text{ of } 1.65 = \text{ Rs. } 174.90$

$\displaystyle \text{Price of tooth-paste, shaving-cream, soap, etc. including Sales Tax } = 230 + 10\% \text{ of } 230 = \text{ Rs. } 253$

$\displaystyle \text{Therefore Total amount to be paid by Mrs. Sharma } = 174.90 + 253 = \text{ Rs. } 427.90$

$\displaystyle \text{Since Mrs. Sharma gave a five-hundred rupee note to the shopkeeper,} \\ \\ \text{the money that the shopkeeper will have to return } = 500 - 427.90 = \text{ Rs. } 72.10$

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Question 5: A person buys an article marked at Rs. 2200. The rate of Sales Tax is 12%. He asks the shopkeeper to reduce the price of the article to such an extent that he does not have to pay anything more than Rs. 2240 including Sales Tax. Calculate the reduction, as percent, needed in the marked price of the article.

Answer:

$\displaystyle \text{Let the cost of the article be reduced to Rs. } x$

$\displaystyle \text{Therefore } x + 12\% \text{ of } x = 2240$

$\displaystyle \text{On solving, we get : } x = 2000$

$\displaystyle \text{Reduced price of the article } = \text{ Rs. } 2000$

$\displaystyle \text{Reduction needed } = 2200 - 2000 = \text{ Rs. } 200$

$\displaystyle \text{Hence. reduction as percent of marked-price } \\ \\ = \frac{\text{Reduction}}{\text{Marked Price}} \times 100 = \frac{200}{2200} \times 100 = 9\frac{1}{11} \%$

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Question 6: The price of an article inclusive of 12% Sales Tax is Rs. 2016. Find its marked price. If the Sales Tax is reduced to 7%, how much less does the customer pay for the article ?

Answer:

$\displaystyle \text{Let marked price be Rs. } x$

$\displaystyle \text{Therefore } x + 12\% \text{ of } x = 2016$

$\displaystyle \text{On solving, we get } : x = 1800$

$\displaystyle \text{Marked price of the article } = \text{Rs. } 1800$

$\displaystyle \text{Since, new Sales Tax } = 7\%$

$\displaystyle \text{Now, the customer will pay } = 1800 + 7\% \text{ of } 1800 = \frac{107}{100} \times 1800 = \text{ Rs. } 1926$

$\displaystyle \text{Therefore customer will pay for the article } = 2016 - 1926 = \text{ Rs. } 90 \text{ less }$

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Question 7: A trader buys an article for Rs. 3600 (inclusive of taxes) Kanpur. He spends Rs. 1200 on traveling, transportation of the article, etc. If he desires a profit of 15 per cent, how much will a customer pay for the article ? The rate of Sales Tax paid by the customer is 8%.

Answer:

$\displaystyle \text{Price paid for the article } = \text{ Rs. } 3600$

$\displaystyle \text{Overheads } = \text{ Rs. } 1200$

$\displaystyle \text{Cost price of the article } = 3600 + 1200 = \text{ Rs. } 4800$

$\displaystyle \text{And, sale-price } = \Big( \frac{100+15}{100} \Big) \text{ of } 4800 = \frac{115}{100} \times 4800 = \text{ Rs. } 5525$

$\displaystyle \text{Money paid by the customer Sale-price of the article + Sales Tax on it } \\ \\ = 5520 + 8\% \text{ of } 5520 = \text{ Rs. } 5961.60$

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Question 8: A shopkeeper buys an article for, Rs. 1500 and spends 20% of the cost on its packing, transportation, etc. Then he marks the article at a certain price. If he sells the article for Rs. 2452.50 including 9% sales Tax on the price marked, find his profit as per cent.

Answer:

$\displaystyle \text{Let marked price of the article be Rs. } x$

$\displaystyle x + \frac{9x}{100} = 2452.50$

$\displaystyle \text{On solving, we get } : x = 2250$

$\displaystyle \text{Marked price of the article }= \text{ Rs. } 2250 = \text{ Its selling price }$

Since, the shopkeeper buys the article for Rs. 1500 and spends 20% of the cost as overheads,

$\displaystyle \text{Total cost price of the article } = 1500 + 20\% \text{ of } 1500 = 1500 + 300 = \text{ Rs. }1800$

$\displaystyle \text{Profit = Selling price - Total cost price } = 2250 - 1800 = \text{ Rs. } 450$

$\displaystyle \text{Profit \% } = \frac{450}{1800} \times 100 = 25\%$

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Question 9: The catalogue price of a computer set is Rs. 45000. The shopkeeper gives a discount of 7% on the listed price. He gives a further off-season discount of 4% on the balance. However, Sales Tax at 8% is charged on the remaining amount. Find :
(i) the amount of Sales Tax a customer has to pay,
(ii) the final price he has to pay for the computer set. [ ICSE Board 2005]

Answer:

$\displaystyle \text{Since, the list Price } = \text{ Rs. } 45000$

$\displaystyle \text{Discount } = 7\% \text{ of } 45000 = \text{ Rs. } 3150$

$\displaystyle \text{Price after discount = List price - Discount } = 45000 - 3150 = \text{ Rs. } 41850$

$\displaystyle \text{Off-season discount } = 4\% \text{ of } 41850 = \text{ Rs. } 1674$

$\displaystyle \text{Sale-price } = 41850 - 1674 = \text{ Rs. } 40176$

$\displaystyle \text{(i) The amount of Sales Tax a customer has to pay } = 8\% \text{ of } 40716 = \text{ Rs. } 3214.08$

$\displaystyle \text{(ii) The final price, the customer has to pay for the computer } \\ \\ \text{ = Sale-price + Sales Tax } = 40176 + 3214.08 = \text{ Rs. } 43390.08$

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Question 10: A person bought an article for Rs. 1374, which included a discount of 15% on the marked price and a sales-tax of 10% on the reduced price. Find the marked price of the article. [ ICSE Board 2007]

Answer:

Since, discount $\displaystyle = 15\%$ and sales tax $\displaystyle = 10\%$

$\displaystyle \text{Price paid = Marked price } \times \Big( \frac{100-15}{100} \Big) \times \Big( \frac{100+10}{100} \Big)$

$\displaystyle \Rightarrow 374 = \text{ Marked price } \times \frac{85}{100} \times \frac{100}{110}$

$\displaystyle \Rightarrow \text{ Marked price } = 374 \times \frac{100}{85} \times \frac{110}{100} = \text{ Rs. } 400$

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Question 11: A shopkeeper buys an article at a rebate of 20% on the printed price. He spends Rs. 40 on transportation of the article. After charging a sales tax of 7% on the printed price, he sells the article for Rs. 1070. Find his gain as percent.

Answer:

$\displaystyle \text{Let printed price of the article be Rs. } x$

According to the given statement :

$\displaystyle x \Big( \frac{100+7}{100} \Big) = 1070 \Rightarrow x = 1000$

$\displaystyle \text{Therefore Printed price of the article = Rs.} 1000$

Given, that the shopkeeper buys the article at 20% rebate

$\displaystyle \text{Therefore For the shopkeeper, C.P. of the article } \\ \\ = 1000 - 20\% \text{ of } 1000 = \text{ Rs. } 800$

Since, he spends Rs. 40 on the transportation of the article

$\displaystyle \text{Total (actual) cost price } = 800 + 40 = \text{ Rs. }840$

$\displaystyle \text{The selling price (excluding sales tax) = printed price } = \text{ Rs. }1000$

$\displaystyle \text{Profit } = 1000 - 840 = \text{ Rs. }160$

$\displaystyle \text{And, Profit} \% = \frac{160}{840} \times 100 = 19\frac{1}{21} \%$

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Question 12: A shopkeeper buys an article at a discount of 30% from the wholesaler (the printed price of the article being Rs. 2000) and paid sales-tax at the rate of 8%. The shopkeeper sells the article to a buyer at the printed price and charges tax at the same rate. Find the VAI (Value Added Tax) paid by the shopkeeper.

Answer:

$\displaystyle \text{Given : Printed price of the article } = \text{ Rs. } 2000$

$\displaystyle \text{and, discount } = 30\% \text{ of } 2000 = \frac{30}{100} \times 2000 = \text{ Rs. } 600$

$\displaystyle \text{Sale price for the wholesale } = (2000-600) = \text{ Rs. } 1400$

$\displaystyle \text{Sales-tax paid by the shopkeeper } = 8\% \text{ of } 1400 = \frac{8}{100} \times 1400 = \text{ Rs. } 112$

$\displaystyle \text{The shopkeeper sells the article for Rs. } 2000$

$\displaystyle \text{Tax charged by the shopkeeper } = 8\% \text{ of } 2000 = \frac{8}{100} \times 2000 = \text{ Rs. } 160$

$\displaystyle \text{VAT paid by the shopkeeper = Tax charged - Tax paid } = 160 - 112 = \text{ Rs. } 48$

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Question 13: A shopkeeper sells an article at its marked price ( Rs. 7500) and charges sales-tax at the rate of 12% from the customer. If the shopkeeper pays a VAT of Rs. 180; calculate the price (inclusive of tax) paid by the shopkeeper.

Answer:

Since, the shopkeeper sells the article for Rs. 7500 and charges sales-tax at the rate of 12%.

$\displaystyle \text{Therefore Tax charged by the shopkeeper } \\ \\ = 12\% \text{ of } 7500 = \frac{12}{100} \times 7500 = \text{ Rs. }900$

VAT = Tax charged – Tax paid $\displaystyle \Rightarrow 180 = 900 - \text{ Tax Paid }$

$\displaystyle \text{Tax paid by the shopkeeper } = 900 - 180 = \text{ Rs. } 720$

If the shopkeeper buys the article for

$\displaystyle \text{Tax on it } = 12\% \text{ of } x = 720 \Rightarrow x = \text{ Rs. }6000$

$\displaystyle \text{The price (inclusive of tax) paid by the shopkeeper } = 6000 +720 = \text{ Rs. }6720$

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Question 14: A person buys an article for Rs. 10000 and pays 7% tax. He sells the same article for
Rs. 13000 and charges 9% tax. Find the VAT paid by this person.

Answer:

$\displaystyle \text{Cost price of the article } = \text{ Rs. } 10000$

$\displaystyle \text{Tax paid by this person} = 7\% \text{ of } 10000 = \frac{7}{100} \times 10000 = \text{ Rs. } 700$

$\displaystyle \text{Selling price of the article } = \text{ Rs. } 13000$

$\displaystyle \text{Tax charged at } 9\% = 9\% \text{ of } 13000 = \frac{9}{100} \times 13000 = \text{ Rs. } 1170$

$\displaystyle \text{VAT = Tax recovered on sale - Tax paid on purchase } = 1170 - 700 = \text{ Rs. } 470$

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Question 15: A manufacturer sells a washing machine to a wholesaler for Rs. 15000. The wholesaler sells it to a trader at a profit of Rs. 1200 and the trader, in turn, sells it to a consumer at a profit of Rs.1900. If the rate of VAT is 8% find:

(i) the amount of VAT received by the State Government on the sale of this machine from the manufacturer and the wholesaler.

(ii) the amount that the consumer pays for the machine. [ ICSE Board 2011]

Answer:

$\displaystyle \text{(i) On selling machine for Rs. }15000; \text{ the tax received by the manufacture } = 8\% \text{ of } 15000 = \frac{8}{100} \times 15000 = \text{ Rs. } 1200$

$\displaystyle \text{Therefore VAT received from the manufacturer } = \text{ Rs. } 1200$

$\displaystyle \text{For wholesaler, C.P. } = \text{ Rs. } 15000$

$\displaystyle \text{S.P. } = 15000 + 1200 = \text{ Rs. } 16200$

$\displaystyle \text{Tax paid } = 8\% of 15000 = \text{ Rs. } 1200$

$\displaystyle \text{and, tax charged } = 8% \text{ of } 16200 = \text{ Rs. } 1296$

$\displaystyle \text{VAT received from wholesaler = Tax charged - Tax paid } \\ \\ =1296 - 1200 = \text{ Rs. } 96$

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Question 16: During a financial year, a shopkeeper purchased goods worth Rs. 415000 and paid a total tax of Rs. 38000. His sales during this period consisted of a taxable turnover of Rs. 50000 for goods taxable at 5% and Rs. 320000 for goods taxable at 12%. He also sold tax exempted goods worth Rs. 45000 during this period. Calculate his tax liability (under VAT) for the financial year.

Answer:

$\displaystyle \text{Turnover of goods taxable at } 5\% = \text{ Rs. }50000$

$\displaystyle \text{Tax charged } = 5\% \text{ of } 50000 = \frac{5}{100} \times 50000 = \text{ Rs. }2500$

$\displaystyle \text{Turnover of goods taxable at } 12\% = \text{ Rs. }320000$

$\displaystyle \text{Tax charged } = 12\% \text{ of } 320000 = \frac{12}{100} \times 320000 = \text{ Rs. }38400$

$\displaystyle \text{Tax exempted sale } = \text{ Rs. }45000$

$\displaystyle \text{Total tax charged } = 2500 + 38400 = \text{ Rs. }40900$

$\displaystyle \text{Tax paid } = \text{ Rs. }38000$

$\displaystyle \text{Tax liability (under VAT) = Total tax charged - Tax paid } \\ \\ = 40900 - 38000 = \text{ Rs. }2900$

Note: Tax exempted sale means the sale which is not liable for tax under VAT.

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Question 17: An article was bought by a distributor for Rs. 15000 (excluding tax). He sold it to a trader for Rs. 20000. The trader sold the article to a retailer for Rs. 22000 (excluding tax). Find the VAT paid by the distributor and by the trader if the tax rate was 10 per cent.

Answer:

For the distributor:

$\displaystyle \text{Cost of the article } = \text{ Rs. }15000$

$\displaystyle \text{Tax paid }= 10\% \text{ of } 15000 = \frac{10}{100} \times 15000 = \text{ Rs. }1500$

$\displaystyle \text{Selling price of the article }= \text{ Rs. }20000$

$\displaystyle \text{Tax charge }= 10\% \text{ of } 20000 = \frac{10}{100} \times 20000 = \text{ Rs. }2000$

$\displaystyle \text{VAT paid by distributor = Tax recovered on sale - Tax paid on purchase } \\ \\ = 2000 - 1500 = \text{ Rs. }500$

For the trader :

$\displaystyle \text{Cost of the article }= \text{ Rs. }20000$

$\displaystyle \text{Tax paid }= 10\% \text{ of } 20000 = \text{ Rs. }2000$

$\displaystyle \text{Selling price of the article }= \text{ Rs. }22000$

$\displaystyle \text{Tax charged }= 10\% \text{ of } 22000 = \frac{10}{100} \times 22000 =\text{ Rs. }2200$

$\displaystyle \text{VAT paid by trader = Tax recovered on sale - Tax paid on purchase } \\ \\ = 2200 - 2000 = \text{ Rs. }200$

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Question 18: A manufacturing company sold a commodity to its distributor for Rs. 22000 including VAT. The distributor sold the commodity to a retailer for Rs. 22000 excluding tax and the retailer sold it to a consumer for Rs. 25000 plus tax (under VAT). If the rate of ax at each stage is 10%, what was the:
(i) sale price of the commodity for the manufacturer ?
(ii) the amount of VAT paid by the retailer ?

Answer:

$\displaystyle \text{(i) Let the sale price of the commodity for the manufacturer be Rs. } x$

$\displaystyle \text{Therefore } x + \frac{10x}{100} = 22000$

$\displaystyle \text{On solving, we get} : x = \text{ Rs. }20000$

$\displaystyle \text{Therefore the sale price of the commodity for the manufacturer } = \text{ Rs. }20000$

$\displaystyle \text{(ii) For the retailer : }$

$\displaystyle \text{C.P. = S.P. for distributor }= \text{ Rs. }22000$

$\displaystyle \text{and, S.P. } = \text{ Rs. }25000$

$\displaystyle \text{Therefore VAT = Tax on (S.P. - C.P.) = } \frac{10}{100} \times ( 25000-22000) = \text{ Rs. }300$

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Question 19: The printed price of an article is Rs. 60000. The wholesaler allows a discount of 20% to the shopkeeper. The shopkeeper sells the article to the customer at the printed price. Sales tar (under VAT) is charged at the rate of 6% at every stage. Find :

(i) the cost to the shopkeeper inclusive of tax

(ii) VAT paid by the shopkeeper to the Government

(iii) the cost to the customer inclusive of tax [ ICSE Board 2012]

Answer:

For wholesaler:

$\displaystyle \text{Printed price } = \text{ Rs. }60000$