Question 1

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 2

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 3

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.

Question 4

A man sells 3 types of articles at 10%, 20% and 30% profit respectively. If the ratio of the cost of the articles is 1 : 2 : 3 and the ratio of the number of articles of each type sold is 3 : 2 : 1, then what is his net profit?

Accepted Answer

Concept & Weighted Average: The net profit percentage on multiple types of items can be found by calculating the total profit generated and dividing it by the total cost price incurred. Net Profit % = ( \frac{Total Profit}{Total Cost} ) × 100 Step-by-Step Solution: 1. Let the cost price (CP) of the 3 types of articles be 1x, 2x, and 3x. 2. Let the number of articles sold of each type be 3y, 2y, and 1y. 3. Calculate the Total Cost (Total CP): - Total CP of Type 1 = 1x × 3y = 3xy - Total CP of Type 2 = 2x × 2y = 4xy - Total CP of Type 3 = 3x × 1y = 3xy - Total CP = 3xy + 4xy + 3xy = 10xy 4. Calculate the Total Profit: - Profit on Type 1 (10%) = 10% of 3xy = 0.3xy - Profit on Type 2 (20%) = 20% of 4xy = 0.8xy - Profit on Type 3 (30%) = 30% of 3xy = 0.9xy - Total Profit = 0.3xy + 0.8xy + 0.9xy = 2.0xy 5. Calculate the Net Profit Percentage: Net Profit % = ( (2.0xy/10xy) ) × 100 = 20% Exam Strategy & Shortcut: Assume convenient numbers instead of variables. Let costs be ₹100, ₹200, ₹300 and quantities be 3, 2, 1. Total cost = 300 + 400 + 300 = 1000. Total profit = 10% of 300 + 20% of 400 + 30% of 300 = 30 + 80 + 90 = 200. Net Profit % = (200/1000) × 100 = 20%. Common Pitfall: Simply averaging the profit percentages (10% + 20% + 30%) / 3 = 20%. Although this gives the correct numerical answer by pure coincidence in this specific problem (due to symmetrical weighting), this method is fundamentally flawed and will fail in most other scenarios. Always use weighted sums. Final Answer: Therefore, the correct answer is 20%.

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