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%
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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