Discussion
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
Answer: C
The alligation rule gives the ratio in which two ingredients must be mixed:
\[ \frac{\text{cheaper quantity}}{\text{dearer quantity}} = \frac{\text{dearer} - \text{mean}}{\text{mean} - \text{cheaper}} \]
Treat the profit percentages as the two "prices".
\[ \frac{\text{8\% part}}{\text{18\% part}} = \frac{18 - 14}{14 - 8} = \frac{4}{6} = \frac{2}{3} \]
So the 1000 kg splits into 2 and 3 of 5 parts:
\[ \text{18\% part} = \frac{3}{5} \times 1000 = 600 \text{ kg} \]
The overall 14% is nearer 18 than 8, so the higher-profit portion must be the larger - a check on which share is which.
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