Two-thirds of a consignment was sold at a profit of 6% and the rest at a loss of 3%. If however there was an overall profit of ₹ 540, the value of consignment was

### Concept & Weighted Profit The overall profit or loss on a consignment can be calculated by summing the profit or loss from each fractional part. $$ \text{Overall Profit} = P_1 + P_2 - L_3 \dots $$ ### Step-by-Step Solution * Let the total value of the consignment be $x$. * Profit on two-thirds of the consignment: $\frac{2}{3}x \times 6\% = 0.04x$. * The rest of the consignment is $1 - \frac{2}{3} = \frac{1}{3}$. * Loss on the remaining one-third: $\frac{1}{3}x \times 3\% = 0.01x$. * Overall Profit = Profit - Loss = $0.04x - 0.01x = 0.03x$. * We are given that the overall profit is ₹ 540. * Equating them: $0.03x = 540 \Rightarrow x = \frac{540}{0.03} = 18000$. ### Exam Strategy & Shortcut Use an assumed value like $x = 300$ for easy fraction division. $\frac{2}{3}$ of 300 is 200 (6% profit = +12). $\frac{1}{3}$ of 300 is 100 (3% loss = -3). Net = +9. If net profit is 9, total is 300. Since actual profit is 540 ($9 \times 60$), total is $300 \times 60 = 18000$. ### Common Pitfall Adding the percentages directly without weighting them by their respective fractional amounts of the consignment. ### Final Answer Therefore, the correct answer is **₹ 18000**.