Question 1

A shopkeeper sells a badminton racket, whose marked price is ₹ 30, at a discount of 15% and gives a shuttle cock costing ₹ 1.50 free with each racket. Even then he makes a profit of 20%. His cost price per racket is

Accepted Answer

Concept & Total Cost Inclusion: When a free item is given with a purchase, the Cost Price to the shopkeeper must include the cost of both the main item and the free item to accurately calculate the overall profit. Step-by-Step Solution: - Marked Price (MP) of the racket = Rs. 30. - Discount given on racket = 15%. - Selling Price (SP) of the racket = 30 - (15% of 30) = 30 - 4.50 = Rs. 25.50. - The customer pays Rs. 25.50 in total. This is the shopkeeper's total revenue. - Let the Cost Price (CP) of the racket be x. - The shopkeeper gives a free shuttlecock costing Rs. 1.50. - Total Cost Price for the shopkeeper = CP of racket + Cost of shuttlecock = x + 1.50. - The shopkeeper makes an overall profit of 20% on his total investment. - Total Revenue (SP) = Total Cost × (1 + \frac{Profit%}{100}). - 25.50 = (x + 1.50) × 1.20. - 25.50 = 1.20x + (1.50 × 1.20). - 25.50 = 1.20x + 1.80. - 1.20x = 25.50 - 1.80 = 23.70. - x = (23.70/1.20) = (237/12) = 19.75. - The cost price of the racket itself (x) is Rs. 19.75. Exam Strategy & Shortcut: Calculate Total Revenue: 30 × 0.85 = 25.50. Calculate Total Cost: Revenue / 1.2 = 25.50 / 1.2 = 21.25. Total Cost includes the racket and the shuttlecock. CP of racket = Total Cost - Cost of shuttlecock = 21.25 - 1.50 = 19.75. Common Pitfall: Failing to include the cost of the free shuttlecock in the shopkeeper's Total Cost base, or mistakenly subtracting it from the Selling Price instead of adding it to the Cost Price. Final Answer: Therefore, the correct answer is ₹ 19.75.

Question 2

A shopkeeper sells 25 articles at ₹ 45 per article after giving 10% discount and earns 50% profit. If the discount is not given, the profit gained is

Accepted Answer

Concept & Discount Logic: The number of articles sold is redundant information when dealing purely with uniform percentages. Focus on a single article. MP = \frac{SP}{1 - D%} Step-by-Step Solution: • Let's consider a single article. The given Selling Price (SP) after a 10% discount is ₹ 45. • Marked Price (MP) = (45/0.90) = 50. • The profit earned at this SP (₹ 45) is 50%. • Cost Price (CP) = (45/1.50) = 30. • If no discount is given, the article is sold at its Marked Price, so the new SP = ₹ 50. • New Profit = MP - CP = 50 - 30 = 20. • New Profit % = (20/30) × 100 = 66 (2/3)%. Exam Strategy & Shortcut: Using the ratio formula \frac{MP}{CP} = (100 + P%/100 - D%) \frac{MP}{CP} = (150/90) = (5/3) If sold at MP (no discount), profit is (5-3/3) = (2/3) = 66 (2/3)%. The ₹ 45 and 25 articles are completely irrelevant. Common Pitfall: Using the 25 articles to find total SP (₹ 1125) and proceeding with large numbers. This slows down the calculation significantly without changing the final percentage. Final Answer: Therefore, the correct answer is 66 (2/3)%.

Question 3

A shopkeeper sold sarees at ₹ 266 each after giving 5% discount on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?

Accepted Answer

Concept & Marked Price Determination: We first determine the Marked Price (labelled price) from the discounted Selling Price, then use the "no discount" scenario to find the Cost Price. MP = \frac{SP}{1 - D%} Step-by-Step Solution: • The Selling Price (SP) of each saree after a 5% discount is ₹ 266. • Marked Price (MP) = (266/1 - 0.05) = (266/0.95) = 280. • Had he not given the discount, he would sell the saree at the MP, meaning the new SP = ₹ 280. • At this new SP, the profit would be 12% on the Cost Price (CP). • Cost Price (CP) = \frac{New SP}{1 + P%} = (280/1.12). • Solving for CP: (280/1.12) = (28000/112) = 250. • The cost price is ₹ 250, which does not match options (a), (b), or (c). Exam Strategy & Shortcut: Calculate MP = (266/0.95). Notice that 266 = 133 × 2 = 19 × 7 × 2. Since 95 = 19 × 5, (266/95) simplifies cleanly to (14/5) = 2.8, making MP = 280. Then CP = (280/1.12) = 250. Fast mental calculation of these ratios saves time. Common Pitfall: Selecting "Data inadequate" when the calculated answer doesn't appear in the numeric choices, rather than correctly choosing "None of these". Final Answer: Therefore, the correct answer is None of these.

Question 4

If the selling price of an article is five times the discount offered and if the percentage of discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.

Accepted Answer

Concept & Relationship between SP, MP, CP, and Discount: The core relationship connects the variables: Marked Price (MP) = Selling Price (SP) + Discount (D) and Selling Price (SP) = Cost Price (CP) + Profit (P). Discount % = (D/MP) × 100 Profit % = (P/CP) × 100 Step-by-Step Solution: • Given: SP = 5D. • Since MP = SP + D, we have MP = 5D + D = 6D. • Calculate Discount Percentage: Discount % = (D/6D) × 100 = (100/6)% = 16.66%. • We are given that Profit % = Discount %. So, Profit % = (100/6)% = (1/6) as a fraction. • This means Profit P = (1/6) of CP. • Since SP = CP + P, we substitute: SP = CP + \frac{CP}{6} = \frac{7CP}{6}. • We know from the beginning that SP = 5D. • Equating both expressions for SP: 5D = \frac{7CP}{6}. • Rearranging to find the ratio of Discount to Cost Price: (D/CP) = (7/5 × 6) = (7/30). Exam Strategy & Shortcut: Express everything in terms of fractions based on D. SP = 5D, MP = 6D, so discount fraction is 1/6. Since profit fraction is also 1/6, CP must be scaled such that adding 1/6 of itself yields 5D. CP × (7/6) = 5D \Rightarrow D/CP = 7/30. Common Pitfall: Confusing the base for the percentages. Discount is always calculated on the Marked Price (MP), not the Selling Price (SP), while Profit is always calculated on the Cost Price (CP). Final Answer: Therefore, the correct answer is 7 : 30.

Question 5

Peter bought an item at 20% discount on its original price. He sold it with 40% increase on the price he bought it. The new sale price is by what percent more than the original price?

Accepted Answer

Concept & Successive Percentages: This problem evaluates percentage changes sequentially based on shifting base values (Original Price \rightarrow Cost Price \rightarrow Selling Price). SP = Original Price × (1 - Discount) × (1 + Markup) Step-by-Step Solution: • Let the original price of the item be 100. • Peter bought it at a 20% discount. • Cost Price (CP) for Peter = 100 - (20% of 100) = 80. • He sold it with a 40% increase on the price he bought it (CP). • Increase amount = 40% of 80 = 32. • New Sale Price (SP) = 80 + 32 = 112. • The difference between the new sale price and the original price = 112 - 100 = 12. • Percentage increase over the original price = (12/100) × 100 = 12%. Exam Strategy & Shortcut: Use the successive percentage change concept with a base of 100. Original = 100. After 20% discount: 80. After 40% markup on 80: 80 × 1.4 = 112. The change from 100 to 112 is exactly 12%. Common Pitfall: Calculating the 40% markup on the original price (100) instead of the discounted price (80), which would incorrectly yield a sale price of 120 and a 20% profit. Final Answer: Therefore, the correct answer is 12.

Question 6

A dealer marked the price of an item 40% above the cost price. He allowed two successive discounts of 20% and 25% to a particular customer. As a result he incurred a loss of ₹448. At what price did he sell the item to the said customer?

Accepted Answer

Concept & Logic: Successive discounts are calculated sequentially on the marked price. Let the Cost Price (CP) be 100x to simplify percentage calculations. Step-by-Step Solution: 1. Let the Cost Price (CP) be 100x. 2. The Marked Price (MP) is 40% above CP: MP = 100x + 40x = 140x 3. Two successive discounts of 20% and 25% are given on the MP. Equivalent multiplier for discounts = (1 - 0.20) × (1 - 0.25) = 0.80 × 0.75 = 0.60 Selling Price (SP) = 140x × 0.60 = 84x 4. The dealer incurred a loss of ₹448. Loss = CP - SP 100x - 84x = 448 16x = 448 x = (448/16) = 28 5. Find the Selling Price: SP = 84x = 84 × 28 = 2352 Exam Strategy & Shortcut: Net discount for 20% and 25% = -20 - 25 + ((-20)(-25)/100) = -45 + 5 = -40%. So, SP = 60% of MP. MP = 140% of CP. SP = 60% of 140% of CP = 84% of CP. Loss = 16% of CP. Given 16% of CP = 448. We need to find 84% of CP. SP = (448/16) × 84 = 28 × 84 = 2352. Common Pitfall: A common mistake is adding successive discounts directly (20% + 25% = 45%) instead of applying them sequentially, which leads to an incorrect selling price. Final Answer: Therefore, the correct answer is ₹ 2,352.

Question 7

Raza purchased a bicycle for ₹ 6810. He had paid a VAT of 13.5%. The list price of the bicycle was

Accepted Answer

Concept & Formula: Value Added Tax (VAT) is calculated as a percentage of the list price (or marked price) and is added to it to determine the final selling price paid by the customer. Final Price = List Price × (1 + (VAT%/100)) Step-by-Step Solution: 1. Let the list price of the bicycle be x. 2. The VAT paid is 13.5% of the list price. 3. The total amount paid by Raza is the sum of the list price and the VAT. x + 13.5% of x = 6810 x (1 + (13.5/100)) = 6810 1.135x = 6810 4. Solve for x: x = (6810/1.135) Multiply numerator and denominator by 1000 to remove the decimal: x = (6810000/1135) x = 6000 Exam Strategy & Shortcut: Treat the list price as 100%. With a 13.5% VAT, the final price is 113.5%. 113.5% corresponds to 6810. 1% corresponds to (6810/113.5) = 60. 100% corresponds to 60 × 100 = 6000. Common Pitfall: A common mistake is calculating 13.5% of the final purchasing price (6810) and subtracting it, rather than setting up the equation where VAT is based on the unknown base list price. Final Answer: Therefore, the correct answer is ₹ 6000.

Question 8

Subroto sold an article for ₹ 528 after allowing a discount of 12% on its marked price. What was the marked price of the article?

Accepted Answer

Concept & Formula: The Selling Price (SP) is calculated by subtracting the discount from the Marked Price (MP). The discount is always calculated as a percentage of the Marked Price. SP = MP × (1 - \frac{Discount%}{100}) Step-by-Step Solution: 1. Let the Marked Price (MP) of the article be x. 2. Discount allowed = 12%. 3. Selling Price (SP) after the discount is ₹ 528. 4. Set up the equation: x × (100% - 12%) = 528 x × 88% = 528 0.88x = 528 5. Solve for x: x = (528/0.88) Multiply the numerator and the denominator by 100 to remove the decimal: x = (52800/88) x = 600 Exam Strategy & Shortcut: If 12% is the discount, the customer pays 88% of the marked price. 88% \equiv 528 Divide by 88 to find 1%: 1% \equiv 6 Multiply by 100 to find 100% (the Marked Price): 100% \equiv 600. Common Pitfall: A common pitfall is calculating 12% of the selling price (528) and adding it back, which mathematically yields the wrong base value. Discount is strictly applied on the Marked Price. Final Answer: Therefore, the correct answer is ₹ 600.

Question 9

Supriya sold a washing machine for ₹ 8500. She incurred a loss of 15% in this transaction. At what price had she bought the washing machine?

Accepted Answer

Concept & Formula: The Cost Price (CP) can be calculated directly from the Selling Price (SP) and the loss percentage using the formula: CP = (SP/1 - \frac{Loss%){100}} Step-by-Step Solution: 1. Identify the given values: Selling Price (SP) = ₹ 8500 Loss Percentage = 15% 2. Set up the equation: A loss of 15% means the SP is 85% of the CP. SP = 85% of CP 8500 = 0.85 × CP 3. Solve for CP: CP = (8500/0.85) Multiply numerator and denominator by 100: CP = (850000/85) = 10000 Exam Strategy & Shortcut: If SP represents 85%, then 85% = 8500. 1% = 100. 100% (which is CP) = 100 × 100 = 10000. Common Pitfall: A very common mistake is calculating 15% of the Selling Price (8500) and adding it to the SP, which results in 8500 + 1275 = 9775. Loss must always be calculated on the Cost Price. Final Answer: Therefore, the correct answer is ₹ 10000.

Question 10

The price of a cycle is marked at ₹ 1150. A shopkeeper earns a profit of 15% after allowing a discount of 15% on the marked price. Find the cost price of the cycle.

Accepted Answer

Concept & Formula: There is a direct proportional relationship between Marked Price (MP), Cost Price (CP), Profit%, and Discount%: (MP/CP) = (100 + Profit%/100 - Discount%) Step-by-Step Solution: 1. Identify the given values: Marked Price (MP) = ₹ 1150 Profit = 15% Discount = 15% 2. Use the direct ratio formula: (1150/CP) = (100 + 15/100 - 15) (1150/CP) = (115/85) 3. Solve for CP: CP = (1150 × 85/115) CP = 10 × 85 = 850 Exam Strategy & Shortcut: Using the formula (MP/CP) = (100+P/100-D) is the fastest way. The numbers 115 and 85 immediately simplify against the 1150 MP. Common Pitfall: Assuming that a 15% profit and 15% discount cancel each other out, making the CP equal to the MP. They are applied to different bases. Final Answer: Therefore, the correct answer is ₹ 850.

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