Sam purchased 20 dozens of toys at the rate of ₹ 375 per dozen. He sold each one of them at the rate of ₹ 33. What was his percentage profit?

### Concept & Consistent Units To calculate profit percentage, the Cost Price (CP) and Selling Price (SP) must be for the exact same quantity. If CP is given in dozens and SP in single units, convert both to a single unit (or both to a dozen) before calculating. $$ \text{Profit \%} = \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100 $$ ### Step-by-Step Solution Given: * CP per dozen = ₹ 375 * Quantity purchased = 20 dozens (Note: This is extra information not needed for the percentage calculation if we use per-unit values). * SP per toy = ₹ 33 * 1 dozen = 12 toys Calculation: 1. Calculate the Cost Price (CP) for a single toy. $$ \text{CP per toy} = \frac{375}{12} = 31.25 $$ 2. Calculate the profit per toy. $$ \text{Profit} = \text{SP} - \text{CP} = 33 - 31.25 = 1.75 $$ 3. Calculate the profit percentage based on the CP per toy. $$ \text{Profit \%} = \left(\frac{1.75}{31.25}\right) \times 100 $$ 4. Eliminate decimals by multiplying numerator and denominator by 100. $$ \text{Profit \%} = \left(\frac{175}{3125}\right) \times 100 $$ 5. Simplify the fraction by dividing by 25. $$ \text{Profit \%} = \left(\frac{7}{125}\right) \times 100 = \frac{700}{125} $$ 6. Divide to find the final percentage. $$ \frac{700}{125} = 5.6 $$ ### Exam Strategy & Shortcut Instead of finding per-unit cost, convert SP to per-dozen to avoid dividing 375 by 12. SP per dozen = $33 \times 12 = 396$. Profit per dozen = $396 - 375 = 21$. Profit % = $(21 / 375) \times 100$. Divide 21 and 375 by 3 to get $(7 / 125) \times 100 = 700 / 125 = 5.6\%$. This avoids decimals completely until the final step. ### Common Pitfall Calculating the total CP ($20 \times 375 = 7500$) and total SP ($20 \times 12 \times 33 = 7920$) creates large numbers that are harder to subtract and divide ($420/7500$), costing valuable time on an exam. ### Final Answer Therefore, the correct answer is **5.6**.