Discussion
In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Answer: A
The alligation rule gives the ratio in which two ingredients must be mixed:
\[ \frac{\text{cheaper quantity}}{\text{dearer quantity}} = \frac{\text{dearer} - \text{mean}}{\text{mean} - \text{cheaper}} \]
\[ \frac{\text{Rs. 6 rice}}{\text{Rs. 8.75 rice}} = \frac{8.75 - 7.50}{7.50 - 6} = \frac{1.25}{1.50} = \frac{5}{6} \]
The mean of 7.50 sits slightly nearer the dearer price, so a little more of the expensive rice is needed - consistent with 5 : 6.
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