CBSE Class 8 Mathematics Comparing Quantities Assignment Set 07

Discount

Question 1. The cost of a medicine is Rs 980. The chemist is giving a discount of 15%. Find the selling price of the medicine.
Answer: Marked Price (MP) = Rs 980
Discount percentage = \(15\%\)
Discount amount = \(15\% \text{ of Rs } 980 = \frac{15}{100} \times 980 = \text{Rs } 147\)
Selling Price (SP) = Marked Price - Discount
SP = \(980 - 147 = \text{Rs } 833\)
In simple words: The selling price is found by subtracting the discount amount from the original marked price.

Exam Tip: Always subtract the discount from the marked price to get the selling price.

Question 2. The cost of a T.V is Rs 18500. During festival season, a discount of 15% is allowed on it. Find the discount and its sale price.
Answer: Marked Price (MP) = Rs 18500
Discount percentage = \(15\%\)
Discount amount = \(15\% \text{ of Rs } 18500 = \frac{15}{100} \times 18500 = \text{Rs } 2775\)
Sale Price = Marked Price - Discount
Sale Price = \(18500 - 2775 = \text{Rs } 15725\)
In simple words: First calculate 15% of the total cost, then subtract it to find the final sale price.

Exam Tip: Clearly label both parts of your final answer: the discount amount and the sale price.

Question 3. A fan is marked for Rs 1800. During off season a discount of 20% is given. Find its sale price.
Answer: Marked Price (MP) = Rs 1800
Discount percentage = \(20\%\)
Discount amount = \(20\% \text{ of Rs } 1800 = \frac{20}{100} \times 1800 = \text{Rs } 360\)
Sale Price = Marked Price - Discount
Sale Price = \(1800 - 360 = \text{Rs } 1440\)
In simple words: Subtract the 20% discount from the marked price to get the price paid by the customer.

Exam Tip: You can also find the sale price directly by calculating \(80\%\) of the marked price: \(0.80 \times 1800 = \text{Rs } 1440\).

Question 4. The cost of a cooler is Rs 5000. During off season, a discount is given and was sold for Rs 4250. Find the rate of discount.
Answer: Marked Price (MP) = Rs 5000
Selling Price (SP) = Rs 4250
Discount amount = Marked Price - Selling Price
Discount amount = \(5000 - 4250 = \text{Rs } 750\)
Discount percentage = \(\left(\frac{\text{Discount}}{\text{Marked Price}}\right) \times 100\)
Discount percentage = \(\left(\frac{750}{5000}\right) \times 100 = 15\%\)
In simple words: Find the money saved by subtracting the sale price from the original price, then convert it into a percentage of the original price.

Exam Tip: Percentage discount is always calculated on the marked price, never on the selling price.

Question 5. An article was sold for Rs 972 after allowing 15% discount. Find its marked price.
Answer: Selling Price (SP) = Rs 972
Discount percentage = \(15\%\)
Let the marked price be \(x\).
Selling Price = Marked Price - Discount
\(SP = x - (15\% \text{ of } x)\)
\(972 = x - 0.15x\)
\(972 = 0.85x\)
\(x = \frac{972}{0.85} = \frac{97200}{85} = \text{Rs } 11320\)
In simple words: Since the selling price is 85% of the marked price, divide the selling price by 0.85 to find the original marked price.

Exam Tip: When working backward from selling price to marked price, do not just take 15% of the selling price; use the algebraic equation or multiplier method.

Question 6. An article is marked 20% above the cost price. The shopkeeper allows a discount of 12% on it. Find his gain or loss per cent.
Answer: Let the Cost Price (CP) be Rs 100.
Marked Price (MP) = \(CP + 20\% \text{ of } CP = 100 + 20 = \text{Rs } 120\)
Discount = \(12\% \text{ of MP} = \frac{12}{100} \times 120 = \text{Rs } 14.40\)
Selling Price (SP) = Marked Price - Discount
\(SP = 120 - 14.40 = \text{Rs } 105.60\)
Since SP > CP, there is a gain.
Gain = \(SP - CP = 105.60 - 100 = \text{Rs } 5.60\)
Gain percentage = \(\left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 = \left(\frac{5.60}{100}\right) \times 100 = 5.6\%\)
In simple words: Assume the cost price is 100, calculate the marked price and selling price step by step, and find the percentage profit.

Exam Tip: Assuming the cost price to be 100 makes percentage calculations much simpler and faster.

Question 7. A shopkeeper marked an article for Rs 420 each. But he says "buy one and get one free article" and still he gains 5%. Find the C.P. of the article.
Answer: Marked Price of one article = Rs 420
Under the scheme "buy one and get one free", the customer gets 2 articles for the price of 1.
Total Selling Price for 2 articles = Rs 420
Let the Cost Price of 1 article be \(CP\).
Total Cost Price for 2 articles = \(2 \times CP\)
Profit = \(5\%\)
Selling Price = \(Cost Price \times \left(1 + \frac{\text{Profit } \%}{100}\right)\)
\(420 = 2 \times CP \times \left(1 + \frac{5}{100}\right)\)
\(420 = 2 \times CP \times 1.05\)
\(420 = 2.10 \times CP\)
\(CP = \frac{420}{2.10} = \text{Rs } 200\)
In simple words: The shopkeeper sells two items for the price of one, and this total selling price gives him a 5% profit over the cost of two items.

Exam Tip: Remember that "buy one get one free" means the customer pays for 1 item but takes home 2 items, which forms the total selling price.

Question 8. A shopkeeper charged Rs 1242 for a fan which includes 8% VAT on it. Find the original price of the fan.
Answer: Let the original price of the fan be \(x\).
VAT = \(8\% \text{ of } x\)
Total price including VAT = Original Price + VAT
\(1242 = x + 0.08x\)
\(1242 = 1.08x\)
\(x = \frac{1242}{1.08} = \frac{124200}{108} = \text{Rs } 1150\)
In simple words: The given price includes tax, so divide the total amount by 1 plus the tax rate to find the original price before tax.

Exam Tip: VAT and sales tax are added to the list price, so the price before tax is always less than the final bill amount.

Question 9. I purchased an article for Rs 5400 including 8% VAT. Find the price before VAT was added.
Answer: Let the price before VAT be \(x\).
Total price including VAT = \(x + 8\% \text{ of } x\)
\(5400 = x + 0.08x\)
\(5400 = 1.08x\)
\(x = \frac{5400}{1.08} = \frac{540000}{108} = \text{Rs } 5000\)
In simple words: Divide the total purchase price by 1.08 to remove the 8% VAT and find the original cost.

Exam Tip: Always verify your answer by calculating 8% of your calculated price and adding it back to check if it equals the total.

Question 10. The cost of pair of shoes is Rs 4500. The sales tax charged was \(7\frac{1}{2}\%\). Find the amount of the bill.
Answer: Cost of shoes = Rs 4500
Sales tax percentage = \(7\frac{1}{2}\% = 7.5\% = 0.075\)
Sales tax amount = \(7.5\% \text{ of Rs } 4500 = \frac{7.5}{100} \times 4500 = \text{Rs } 337.50\)
Total amount of the bill = Cost of shoes + Sales tax
Total amount = \(4500 + 337.50 = \text{Rs } 4837.50\)
In simple words: Convert the mixed fraction percentage into a decimal, calculate the tax amount, and add it to the original cost.

Exam Tip: Be careful with fractional percentages like \(7\frac{1}{2}\%\); convert them to decimals (7.5%) before performing calculations.