Padam purchased 30 kg of rice at the rate of ₹ 17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of ₹ 18.60 per kg and made 20% overall profit. At what price per kg did he purchase the lot of another 30 kg rice? (N.M.A.T., 2006)

### Concept & Profit and Loss To find the cost price of an unknown component in a mixture when the final selling price and overall profit are given, we must first reverse-calculate the overall average cost price. $$Average\ CP = \frac{Selling\ Price}{1 + \frac{Profit\ \%}{100}}$$ ### Step-by-Step Solution * **Average Selling Price (SP)** of the mixture = ₹ 18.60 per kg * **Overall Profit** = 20% * **Average Cost Price (CP)** of the mixture = $\frac{18.60}{1.20} = 15.50$ per kg * Since the quantities of both types of rice are equal (30 kg each), the average CP is just the simple arithmetic mean of the two individual prices. * Let the price of the second lot of rice be $x$. * $\frac{17.50 + x}{2} = 15.50$ * $17.50 + x = 31.00$ * $x = 31.00 - 17.50 = 13.50$ ### Exam Strategy & Shortcut Recognize that equal weights (30 kg each) mean the overall cost price is perfectly centered between the two individual prices. $18.60$ with a $20\%$ markup implies a cost of $15.50$. The difference between $17.50$ and $15.50$ is $2.00$. The other price must be symmetrically opposite, so $15.50 - 2.00 = 13.50$. ### Common Pitfall A frequent error is calculating the 20% profit on the selling price instead of the cost price, leading to an incorrect average CP of $18.60 \times 0.80 = 14.88$. ### Final Answer Therefore, the correct answer is **₹ 13.50**.