Discussion
Two types of rice costing ₹25 and ₹40 per kg are mixed in the ratio 2 : 3. What is the cost of the mixture per kg?
Answer: B
Correct answer: ₹34
The cost of a mixture is the weighted average of the component prices: \[ \text{mean} = \frac{2 \times 25 + 3 \times 40}{2 + 3} = \frac{50 + 120}{5} = \frac{170}{5} = 34. \] The mixture costs 34 per kg. The distractor 32.50 is the simple average of 25 and 40, correct only for equal quantities. Since more of the dearer rice is used, the answer must lie above the midpoint - which rules out 32.50 and 33 immediately, and is worth checking before any calculation. This is the direct form of the problem; alligation solves the inverse, finding the ratio when the mean is given. The relation is the same read either way, and being able to move in both directions is what the topic amounts to: \[ \frac{q_{1}}{q_{2}} = \frac{p_{2} - m}{m - p_{1}}. \] Substituting the answer back confirms it: \( \frac{40-34}{34-25} = \frac{6}{9} = \frac{2}{3} \).
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