Discussion
Chandan buys some sugar at Rs. 15 per kg. He mixes it with sugar having price Rs. 18 per kg. The final mixture becomes worth Rs. 16 per kg. What is the ratio of quantities of type 1 sugar to type 2 sugar?
Answer: A
The alligation rule gives the ratio in which two ingredients must be mixed:
\[ \frac{\text{cheaper quantity}}{\text{dearer quantity}} = \frac{\text{dearer} - \text{mean}}{\text{mean} - \text{cheaper}} \]
\[ \frac{\text{Rs. 15 sugar}}{\text{Rs. 18 sugar}} = \frac{18 - 16}{16 - 15} = \frac{2}{1} \]
So the ratio is \( 2 : 1 \). The mean price of 16 sits closer to 15 than to 18, so the cheaper sugar must dominate - a check on which way round the ratio goes.
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