A company blends two varieties of tea from two different tea gardens, one variety costing ₹ $20$ per kg and the other ₹ $25$ per kg in the ratio $5 : 4$. He sells the blended tea at ₹ $23$ per kg. Find his profit or loss percent.

### Concept & Weighted Average To find the overall profit or loss percentage, we first need to determine the effective Cost Price (CP) of the mixed tea. This is calculated using the weighted average of the individual prices based on their blending ratio. $$ \text{Weighted CP} = \frac{(Q_1 \times P_1) + (Q_2 \times P_2)}{Q_1 + Q_2} $$ ### Step-by-Step Solution * **Given:** - Price of variety 1 ($P_1$) = ₹ $20$/kg, Ratio quantity ($Q_1$) = $5$ parts - Price of variety 2 ($P_2$) = ₹ $25$/kg, Ratio quantity ($Q_2$) = $4$ parts - Selling Price (SP) of the blend = ₹ $23$/kg * **Calculation:** 1. Calculate the total Cost Price (CP) for $9$ parts ($5 + 4$) of the mixture: Total CP = $(5 \times 20) + (4 \times 25) = 100 + 100 = 200$ 2. Calculate the Cost Price per kg of the mixture: CP per kg = $\frac{200}{9}$ = ₹ $22.22$ 3. Determine if there is a profit or loss. Since SP (₹ $23$) > CP ($\frac{200}{9}$), there is a profit. 4. Calculate the Profit amount per kg: Profit = SP - CP = $23 - \frac{200}{9} = \frac{207 - 200}{9} = \frac{7}{9}$ 5. Calculate the Profit Percentage: Profit % = $\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100$ Profit % = $\frac{\frac{7}{9}}{\frac{200}{9}} \times 100 = \frac{7}{200} \times 100 = \frac{7}{2} = 3.5\%$ ### Exam Strategy & Shortcut Instead of full fractions, use a base of $9$ kg directly. Total cost for $9$ kg = ₹ $200$. Total selling price for $9$ kg = $23 \times 9 = 207$. Profit on ₹ $200$ investment is ₹ $7$. Profit % = $\frac{7}{200} \times 100 = 3.5\%$. This skips the fractional subtraction entirely. ### Common Pitfall A common mistake is taking the simple average of the prices ($\frac{20+25}{2} = 22.5$) instead of the weighted average, which ignores the $5:4$ ratio and leads to an incorrect CP and subsequent profit calculation. ### Final Answer Therefore, the correct answer is **Profit of $3.5\%$**.