Question : Vyom purchased 40 dozen pens at the rate of Rs. 56 per dozen. He sold 15 dozen at a 20% profit and the remaining 25 dozen at a 10% profit. What is his profit percentage?
Option 1: 12.5%
Option 2: 16.66%
Option 3: 11.25%
Option 4: 13.75%
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Correct Answer: 13.75%
Solution : Cost price (CP) = Number of dozens × Rate per dozen = 40 × 56 = Rs. 2240 For the first 15 dozen pens (sold at a 20% profit): Profit percentage = 20% ⇒ Profit per dozen = $\frac{20}{100}$ × Cost per dozen = $\frac{20}{100}×{56}$ = Rs. 11.20 Selling price (SP) per dozen = Cost per dozen + Profit per dozen = 56 + 11.20 = Rs. 67.20 SP for 15 dozen pens = 15 × 67.20 = Rs. 1008 For the remaining 25 dozen pens (sold at a 10% profit i.e. profit of 5.60 per dozen): SP for 25 dozen pens = 25 × 61.60 = Rs. 1540 Total SP = SP for 15 dozen + SP for 25 dozen = 1008 + 1540 = Rs. 2548 Net Profit = SP − CP = 2548 − 2240 = Rs. 308 Profit Percentage = $\frac{\text{Profit}}{\text{CP}}×100$ = $\frac{308}{2240} × 100$ =13.75% Hence, the correct answer is 13.75%.
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