Discussion
In what ratio should a kind of sugar at 8.70 Rs/kg be mixed with another kind of sugar at 9.70 Rs/kg so that the mixture be worth 9 Rs/kg?
Answer: D
The alligation rule gives the ratio in which two ingredients must be mixed:
\[ \frac{\text{cheaper quantity}}{\text{dearer quantity}} = \frac{\text{dearer} - \text{mean}}{\text{mean} - \text{cheaper}} \]
\[ \frac{\text{Rs. 8.70 sugar}}{\text{Rs. 9.70 sugar}} = \frac{9.70 - 9}{9 - 8.70} = \frac{0.70}{0.30} = \frac{7}{3} \]
The mean of 9 lies much nearer 8.70, so the cheaper sugar dominates - consistent with 7 parts to 3.
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