Question

A shopkeeper buys 9 pens for the marked price of 8 pens. He sells each pen after allowing a discount of 5% on the marked price. Find his profit percentage.

• A. 10%
• B. 11.25%
• C. 6.875%
• D. 15%

Answer 1

Answer:

C. 6.875%

Step-by-Step Calculation

• Assume the Marked Price (MP) of 1 pen: Let the MP of 1 pen be ₹100.

• Determine Cost Price (CP): The shopkeeper buys 9 pens for the price of 8 pens. Total MP of 8 pens = 8 × 100 = ₹800. Since he buys 9 pens at this price, the CP of 9 pens is ₹800. Therefore, the CP of 1 pen = 800 / 9.

• Determine Selling Price (SP): He sells each pen at a 5% discount on the MP (₹100). SP of 1 pen = 100 - (5% of 100) = ₹95.

• Calculate Profit per pen: Profit = SP - CP = 95 - (800 / 9). Converting to a common denominator: (855 - 800) / 9 = 55 / 9.

• Calculate Profit Percentage: Profit % = (Profit / CP) × 100 = [(55 / 9) / (800 / 9)] × 100. The '/ 9' terms cancel out, leaving (55 / 800) × 100. This simplifies to 55 / 8 = 6.875%.

Key Concepts for Exams

• Logic for 'Buy X for Price of Y': When Cost Price (CP) equals the Marked Price (MP) of a different quantity, always equate the CP of the actual quantity bought to the MP of the reference quantity.

• Formula: Profit % = [(Selling Price - Cost Price) / Cost Price] × 100.

• Shortcut: If CP of 'a' articles = MP of 'b' articles, and discount is 'd%', Profit % = [((MP of 'b' / CP of 'a') × (100 - d)) - 100]%. In this case: [((8/9) × 95) - 100] = [844.44/9 - 100] = 6.875%.