Class 10: Sales Tax & VAT – ICSE Board Problems – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: The price of a T.V. set inclusive of Sales Tax of 9% is Rs.13407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V. [2002]

Answer:

Let Sales price of the T.V. $\displaystyle = \text{ Rs. } x$

Sales Tax on the T.V. $\displaystyle =9\% \text{ of Rs. } x = 0.09 x$

Total amount paid $\displaystyle x+0.09x = 1.09x = 13407 \Rightarrow x = \text{ Rs. } 12300$

If Sales Tax on the T.V. $\displaystyle =13 \% \text{ of Rs. } 12300$

The customer will have to pay $\displaystyle (13-9)\% \times 12300 = \text{ Rs. } 492$ more.

$\displaystyle \\$

Question 2: The price of a washing machine, inclusive of Sales tax, is Rs.13530. If the Sales Tax is 10% find its basic cost price. [2003]

Answer:

Let Sales Price of the washing machine be $\displaystyle = \text{ Rs. } x$

Total amount paid $\displaystyle = \text{ Rs. } 13530$

Sales Tax $\displaystyle = 10\% \text{ of Rs. } x$

Therefore $\displaystyle x+10\% \text{ of Rs. } x = 13530 \Rightarrow x = \text{ Rs. } 12300$

$\displaystyle \\$

Question 3: The catalog price of a colored T.V. is Rs.24000. The shopkeeper gives a discount of 8% on the list price. He gives a further off season discount of 5% on the balance, But Sales Tax at 10% is charged on the remaining amount. Find:

The sales Tax a customer has to pay.

The final price he has to pay for the T.V. [2001]

Answer:

Catalog price of a colored T.V. $\displaystyle = \text{ Rs. } 24000$

$\displaystyle \text{ Price after} 8\% \text{ discount } = \frac{100-8}{100} \times 24000 = 22080$

$\displaystyle \text{Price after} 5\% \text{off season discount } = \frac{100-5}{100} \times 22080 = \text{ Rs. } 20976$

$\displaystyle \text{Sales Tax } = \frac{10}{100} \times 20976 = \text{ Rs. } 2097.60$

Price paid by the customer $\displaystyle = \text{ Rs. } 20976 + Rs. 2097.60 = \text{ Rs. } 23073.60$

$\displaystyle \\$

Question 4: A manufacturer marks an article at Rs.5000. He sells this article to a wholesaler at a discount of 25% on the marked price and the wholesaler sells it to a retailer at a discount of 15% on its marked price. If the retailer sells the article without any discount and at each stage the sales-tax is 8%, calculate the amount of VAT paid by:

The Wholesaler
The Retailer [2010]

Answer:

Market Price of the article for wholesaler $\displaystyle = \text{ Rs. } 5000$

$\displaystyle \text{Cost Price of the article for wholesaler } = \frac{100-25}{100} \times 5000 =Rs. 3750$

$\displaystyle \text{Amount of tax paid by the wholesaler } = \frac{8}{100} \times 3750 = \text{ Rs. } 300$

$\displaystyle \text{Cost Price of the article for retailer } = \frac{100-15}{100} \times 5000 =Rs. 4250$

$\displaystyle \text{Amount of tax paid by the retailer } = \frac{8}{100} \times 4250 = \text{ Rs. } 340$

Selling price of the article for retailer $\displaystyle = \text{ Rs. } 5000$

$\displaystyle \text{Amount of tax paid by the end customer } = \frac{8}{100} \times 5000 = \text{ Rs. } 400$

Vat paid by retailer $\displaystyle = 400 - 340 = \text{ Rs. } 60$

Vat paid by wholesaler $\displaystyle = 340 - 300 = \text{ Rs. } 40$

$\displaystyle \\$

Question 5: The catalog price of a computer 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 that the customer has to pay ii) the final price he has to pay for the computer set. [2005]

Answer:

Listed Price $\displaystyle = \text{ Rs. } 45000$

$\displaystyle \text{Discount given } = \frac{7}{100} \times 45000 = \text{ Rs. } 3150$

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

$\displaystyle \text{Off season discount } = \frac{4}{100} \times 41850 = \text{ Rs. } 1674$

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

$\displaystyle \\$

Question 6: Dinesh bought an article for Rs. 374, 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. [2007]

Answer:

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

$\displaystyle \text{Discount } = \frac{15}{100} \times x = 0.15x$

Sale price $\displaystyle = x-0.15x = \text{ Rs. } 0.85x$

$\displaystyle \text{Sales tax } = \frac{10}{100} \times 0.85x = \text{ Rs. } 0.085x$

Total price paid by Dinesh $\displaystyle = 0.85x + 0.085x = 0.935x = 374 \Rightarrow x = \frac{374}{0.935} = \text{ Rs. } 400$

$\displaystyle \\$

Question 7: 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 turns sells it to a consumer at a profit of Rs. 1800. 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. [2011]

Answer:

$\displaystyle \text{Tax received by the manufacturer } = \frac{8}{100} \times 1500 = \text{ Rs. } 1200$

For the trader the price $\displaystyle = 15000+1200= \text{ Rs. } 16200$

$\displaystyle \text{Tax paid by the trader } = \frac{8}{100} \times 16200 = \text{ Rs. } 1296$

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

Price for the consumer $\displaystyle = 16200+1800 = \text{ Rs. } 18000$

$\displaystyle \text{Tax paid by the consumer } = \frac{8}{100} \times 18000 = \text{ Rs. } 1440$

Hence the total price paid by the consumer $\displaystyle = 18000+1440 = \text{ Rs. } 19440$

$\displaystyle \\$

Question 8: 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 tax (under VAT) is charged at the rate of 6% at every stage. Find: i) the cost to the shopkeeper inclusive of the tax ii) VAT paid by the shopkeeper to the Government iii) the cost to the customer inclusive of the tax. [2012]

Answer:

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

$\displaystyle \text{Discounted price } = 60000 \times \Big(1- \frac{20}{100} \Big) = \text{ Rs. } 48000$

$\displaystyle \text{Price charged by the wholesaler } = 48000 + \frac{6}{100} \times 48000 = \text{ Rs. } 50880$

The cost to the shopkeeper inclusive of the tax $\displaystyle = \text{ Rs. } 50880$

VAT paid by the shopkeeper = Tax Charged – Tax Paid

$\displaystyle = \frac{6}{100} \times 60000 - \frac{6}{100} \times 48000 = \text{ Rs. } 720$

The cost to the customer inclusive of the tax $\displaystyle = 60000+ 3600 = \text{ Rs. } 63600$

$\displaystyle \\$

Question 9: 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]

Answer:

Printed Price of the camera $\displaystyle = \text{ Rs. } 1600$

Discount $\displaystyle = 20\%$

Sales Tax $\displaystyle = 6\%$

Cost Price of the shopkeeper $\displaystyle = 1600 \times 0.8 = \text{ Rs. } 1280$

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

Sale Price $\displaystyle = \text{ Rs. } 1600$

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

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

VAT $\displaystyle = 96-76.80 = \text{ Rs. } 19.2$

$\displaystyle \\$

Question 10: Tarun 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]

Answer:

Cost Price $\displaystyle = \text{ Rs. } 8000$

Overheads $\displaystyle = \text{ Rs. } 1000$

Listed Price $\displaystyle = \text{ Rs. } 11700$

Sales Tax rate $\displaystyle = 10\%$

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

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

$\displaystyle \\$

Question 11: 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]

Answer:

Listed price $\displaystyle = \text{ Rs. } 1500$

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

Let the price at which the shopkeeper purchased the article $\displaystyle = \text{ Rs. } x$

Therefore

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

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

Total price paid by the shopkeeper $\displaystyle = 1200+144 = \text{ Rs. } 1344$

$\displaystyle \\$

Question 12: 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]

Answer:

Printed Price $\displaystyle = \text{ Rs. } 18000$