The cost of Type 1 rice is ₹ 15 per kg and Type 2 rice is ₹ 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

### Concept & Weighted Average When quantities and their respective prices are given, the price of the mixture is simply the weighted average of the individual prices. $$ \text{Mean Price} = \frac{n_1p_1 + n_2p_2}{n_1 + n_2} $$ ### Step-by-Step Solution 1. Price of Type 1 ($p_1$) = ₹ 15 2. Price of Type 2 ($p_2$) = ₹ 20 3. Ratio of quantities ($n_1 : n_2$) = $2 : 3$. We can assume quantities are 2 kg and 3 kg. 4. Calculate total cost: - Total cost = $(15 \times 2) + (20 \times 3) = 30 + 60 = 90$ 5. Calculate total quantity: - Total quantity = $2 + 3 = 5$ kg 6. Calculate mean price: - Mean price = Total cost / Total quantity = $90 / 5 = \text{₹ } 18$ ### Exam Strategy & Shortcut Using assumed mean: Assume mean is 15. The deviation of Type 2 is $+5$. This $+5$ occurs 3 times (from the ratio), so total deviation is $+15$. Distribute this over the total parts ($2+3=5$): $15 / 5 = +3$. Add to assumed mean: $15 + 3 = 18$. ### Common Pitfall Multiplying the prices by the wrong ratio parts, or adding the prices without weighting them by their respective quantities. ### Final Answer Therefore, the correct answer is **₹ 18**.