Sanket purchased $20$ dozen notebooks at ₹ $48$ per dozen. He sold $8$ dozen at $10\%$ profit and the remaining $12$ dozen with $20\%$ profit. What is his profit percentage in the transaction?

### Concept & Weighted Average Percentage When a total quantity is split into parts and sold at different profit percentages, the overall profit percentage is the weighted average of the individual profit percentages. The base cost price (₹ 48) is uniform across all items, so it cancels out of the percentage calculation. $$\text{Overall Profit } \% = \frac{Q_1P_1 + Q_2P_2}{Q_1 + Q_2}$$ ### Step-by-Step Solution * **Total Quantity:** $20 \text{ dozen}$. * **Quantity 1 ($Q_1$):** $8 \text{ dozen}$. * **Profit 1 ($P_1$):** $10\%$. * **Quantity 2 ($Q_2$):** $12 \text{ dozen}$. * **Profit 2 ($P_2$):** $20\%$. * **Overall Profit Percentage calculation:** $$\frac{8 \times 10\% + 12 \times 20\%}{20}$$ $$= \frac{80 + 240}{20}$$ $$= \frac{320}{20} = 16\%$$ ### Exam Strategy & Shortcut Since the cost price is the same for all items, completely ignore the "₹ 48 per dozen" figure. It is unnecessary data designed to slow you down. The problem simplifies to a pure mixture/weighted average calculation. You can even simplify the ratio of quantities: $8 : 12 = 2 : 3$. Weighted average = $\frac{2(10) + 3(20)}{2 + 3} = \frac{20 + 60}{5} = \frac{80}{5} = 16\%$. ### Common Pitfall A common error is to calculate the exact cost prices and selling prices for all items (Cost = 960, SP1 = 422.4, SP2 = 691.2, Total SP = 1113.6). This yields the right answer but takes substantially more time. ### Final Answer Therefore, the correct answer is **16**.