Question 1: A person buys an unfinished article for Rs.1800 and spends Rs.600 on its finishing, pacing, transportation, etc. He marks the article at such a price that will give him 20% profit. How much will a customer pay for the article including 12% Sales Tax.

Price paid for the unfinished article $\displaystyle = \text{ Rs. } 1800$ $\displaystyle \text{Overheads } = \text{ Rs. } 600$ $\displaystyle \text{Therefore Cost of the article } = \text{ Rs. } 1800 + Rs. 600 = \text{ Rs. } 2400$

Desired profit $\displaystyle = 20\%$ $\displaystyle \text{Sale Price } = \Big( \frac{100+20}{100} \Big) \text{ of Rs. } 2400 = \Big( \frac{100+20}{100} \Big) \times 2400 = \text{ Rs. } 2880$

Therefore Money paid by the customer = Sale Price of the article+Sales Tax on the article $\displaystyle = \text{ Rs. } 2880 + \frac{12}{100} \times 2880 = \text{ Rs. } 3225.60$ $\displaystyle \\$

Question 2: A person buys an article for Rs.800 and spends Rs.100 on its transportation, etc. He marks the article at a certain price and then sells it for Rs.1287 including 10% Sales Tax. Find this profit as a percent.

Price paid for the article $\displaystyle = \text{ Rs. } 800$ $\displaystyle \text{Overheads } = \text{ Rs. } 100$ $\displaystyle \text{Therefore Cost of the article } = \text{ Rs. } 800 + Rs. 100 = \text{ Rs. } 900$

Let the Sale Prices $\displaystyle = x$

Sales Tax on the article $\displaystyle = \frac{10}{100} \times x = 0.1x$

Cost to the customer $\displaystyle = x + 0.1x = 1.1x = 1287 \Rightarrow x = \text{ Rs. } 1170$

Therefore Profit $\displaystyle = 1170-900 = \text{ Rs. } 270$ $\displaystyle \text{Therefore profit} \% = \frac{270}{900} \times 100 = 30\%$ $\displaystyle \\$

Question 3: A person announces a discount of 15% on his goods. If the marked price of an article, in his shop, is Rs.6000; How much a customer has to pay for it, if the rate of Sales Tax is 10%

Marker Price $\displaystyle = \text{ Rs. } 6000$ $\displaystyle \text{Discount } = 15\%$ of the marked price $\displaystyle \text{Discounted Price } = \frac{100-15}{100} \times 6000 = \text{ Rs. } 5100$ $\displaystyle \text{Sales Tax } = \frac{10}{100} \times 5100 = \text{ Rs. } 510$

Price paid by the customer $\displaystyle = 5100 + 510 = \text{ Rs. } 5610$ $\displaystyle \\$

Question 4: 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. 

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 5: A person marks his goods 40% above the cost price and then allows a discount of 20%. Find how much will be a customer pay for an article that costs the person Rs.200 and a Sales Tax of 10% is levied on the sales price of the article.

The cost price $\displaystyle = \text{ Rs. } 200$

Mark Price of goods $\displaystyle = 200+0.4 \times 200= \text{ Rs. } 280$

Discount given $\displaystyle =20\%$ $\displaystyle \text{Discounted Price } = \frac{100-20}{100} \times 280 = \text{ Rs. } 224$ $\displaystyle \text{Amount paid by the customer } 224 + \frac{10}{100} \times 224 = \text{ Rs. } 246.40$ $\displaystyle \\$

Question 6: A toy is purchased for Rs.591.36 which includes 12% rebate on the printed price and 12% Sales Tax on the sales price of the toy. Find the printed price of the toy.

Let the printed Sale Prices $\displaystyle = x$ $\displaystyle \text{After discount the Sale Price } = \frac{100-12}{100} \times x = 0.88x$

Price paid by the customer $\displaystyle = 0.88x+ \frac{12}{100} \times 0.88x = 0.9856x = 591.36 \Rightarrow x = \text{ Rs. } 600.27$ $\displaystyle \\$

Question 7: The catalog price on an article is Rs.20,000. The person allows two successive discounts 15% and 10%. If Sales Tax at the rate of 10% is charged on the remaining amount. Find:

The sales Tax amount a customer has to pay.

The final total price that customer has to pay for the article.

Catalog price of a article $\displaystyle = \text{ Rs. } 20000$ $\displaystyle \text{Price after} 8\% \text{Discount } = \frac{100-15}{100} \times 20000 = 17000$ $\displaystyle \text{Price after } 5\% \text{Discount } = \frac{100-10}{100} \times 17000 = \text{ Rs. } 15300$ $\displaystyle \text{Sales Tax } = \frac{10}{100} \times 15300 = \text{ Rs. } 1530$

Price paid by the customer $\displaystyle = \text{ Rs. } 15300 + Rs. 1530 = \text{ Rs. } 16830$ $\displaystyle \\$

Question 8: A person buys an article of Rs.1700 at a discount of 15% on its printed price. He raises the printed price of the article by 20% and then sells it for Rs.2688 including sales tax on the new marked price. Find:

The rate of sales tax

The trader’s profit as a percent.

Let the printed price $\displaystyle = \text{ Rs. } x$ $\displaystyle \text{Price the trader paid } = \frac{100-15}{100} \times x = 0.85x$

Given $\displaystyle 0.85x = 1700 \Rightarrow x= \text{ Rs. } 2000$ $\displaystyle \text{New Printed Prices } = \frac{100+20}{100} \times 2000 = \text{ Rs. } 2400$

Let the sales tax % $\displaystyle = x$ $\displaystyle \text{Final Selling prices } 2688 = 2400 \Big(1+ \frac{x}{100} \Big) \Rightarrow x = 12\%$

Profit $\displaystyle = 2400-1700 = \text{ Rs. } 700$ $\displaystyle \text{Profit } \%= \frac{700}{1700} \times 100 = 41 \frac{3}{17} \%$ $\displaystyle \\$

Question 9: A person buys an article at a rebate of 20% on its marked price and then spends Rs.300 on its transportation, etc. If he sells the article for Rs.4160 (including sales tax at the rate of 4% of the marked price), find the person’s profit as a percent.

Let the printed price $\displaystyle = \text{ Rs. } x$ $\displaystyle \text{Price the trader paid } = \frac{100-20}{100} \times x = 0.80x$ $\displaystyle \text{Overheads } = \text{ Rs. } 300$ $\displaystyle \text{Sales Tax } = \frac{4}{100} \times x = 0.04x$

Total Price paid by the customer $\displaystyle = 4160$

Therefore $\displaystyle 4160 = x+0.04x \Rightarrow x = \text{ Rs. } 4000$

Total cost paid by the shopkeeper $\displaystyle = 0.8 \times 4000+ 300 = \text{ Rs. } 3500$ $\displaystyle \text{Profit } \% = \frac{4160-3500}{3500} \times 100 = 14 \frac{2}{7} \%$ $\displaystyle \\$

Question 10: A person buys an article for Rs.2400 from a wholesaler at 20% rebate on its list price. He marks up the list price of the article bought by 10% and then sells it for Rs.3498 including sales Tax on the marked-up price. Find:

The rate of sales tax

The person’s profit as a percent.

Let the printed price $\displaystyle = \text{ Rs. } x$ $\displaystyle \text{Price the trader paid } = \frac{100-20}{100} \times x = 0.80x$

Given $\displaystyle 0.80x = 2400 \Rightarrow x= \text{ Rs. } 3000$ $\displaystyle \text{New Printed Prices } = \frac{100+10}{100} \times 3000 = \text{ Rs. } 3300$

Let the sales tax % $\displaystyle = x$ $\displaystyle \text{Final Selling prices } 3498 = 3300 \Big(1+ \frac{x}{100} \Big) \Rightarrow x = 6\%$

Profit $\displaystyle = 3300-2400 = \text{ Rs. } 300$ $\displaystyle \text{Profit } \%= \frac{900}{2400} \times 100 = 37.5\%$ $\displaystyle \\$