Question 1

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 2

When an article was sold for ₹ 696, percent profit earned was $P\%$. When the same article was sold for ₹ 841, percent profit earned was $(p + 25)\%$. What is the value of $P$?

Accepted Answer

Concept & Logic: The difference in the selling prices of an article is directly proportional to the difference in the profit percentages, because both profit percentages are calculated on the same constant Cost Price (CP). Step-by-Step Solution: 1. Identify the Given Data: Selling Price 1 (SP_1) = ₹ 696, Profit = P% Selling Price 2 (SP_2) = ₹ 841, Profit = (P + 25)% 2. Calculate Differences: Difference in Selling Price = SP_2 - SP_1 = 841 - 696 = 145 Difference in Profit Percentage = (P + 25)% - P% = 25% 3. Find the Cost Price (CP): The 25% difference in profit corresponds exactly to the ₹ 145 difference in selling price. 25% of CP = 145 (25/100) × CP = 145 CP = 145 × 4 = 580 4. Calculate Original Profit Percentage (P): In the first case, SP_1 = 696. Profit Amount = SP_1 - CP = 696 - 580 = 116. P = (\frac{Profit}{CP}) × 100 P = ((116/580)) × 100 = ((1/5)) × 100 = 20 Exam Strategy & Shortcut: Equate the percentage change directly to the value change. 25% = 145. 100% = 145 × 4 = 580 (This is the CP). Profit at 696 is 116. Fraction = (116/580) = (1/5) = 20%. Common Pitfall: A common pitfall is forming complex algebraic equations for both SP_1 and SP_2 and trying to substitute, which wastes valuable time instead of simply equating the differences. Final Answer: Therefore, the correct answer is 20.

Question 3

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 4

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 5

Sanjay made a profit of 8% by selling a shirt after offering a discount of 12%. If the marked price of the shirt is ₹ 1080, find its cost price.

Accepted Answer

Concept & Formula: There is a direct proportional relationship linking Marked Price (MP), Cost Price (CP), Discount percentage, and Profit percentage: (MP/CP) = \frac{100 + Profit%}{100 - Discount%} Step-by-Step Solution: 1. Identify the given values: Marked Price (MP) = ₹ 1080, Discount = 12%, Profit = 8%. 2. We need to find the Cost Price (CP). 3. Substitute the values into the direct formula: (1080/CP) = (100 + 8/100 - 12) (1080/CP) = (108/88) 4. Simplify the fraction on the right side: (108/88) = (27/22) 5. Solve for CP: (1080/CP) = (27/22) CP = (1080 × 22/27) CP = 40 × 22 = 880 Exam Strategy & Shortcut: Instead of calculating the Selling Price first (1080 × 0.88 = 950.4) and then dividing by the profit multiplier (950.4 / 1.08 = 880), using the direct ratio formula (MP/CP) = (100+P/100-D) allows for rapid mental calculation and fraction simplification. Common Pitfall: A common mistake is calculating the 8% profit based on the Marked Price rather than the Cost Price, which breaks the fundamental rule of profit and loss. Final Answer: Therefore, the correct answer is 880.

Question 6

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 7

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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