Discussion
Milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively in what ratio the liquids in both the vessels should be mixed to obtain a new mixture in vessel C containing half milk and half water?
Answer: D
The alligation rule gives the ratio in which two ingredients must be mixed:
\[ \frac{\text{cheaper quantity}}{\text{dearer quantity}} = \frac{\text{dearer} - \text{mean}}{\text{mean} - \text{cheaper}} \]
Work with the fraction of milk in each vessel.
\[ A = \frac{4}{7}, \qquad B = \frac{2}{5}, \qquad \text{mixture} = \frac{1}{2} \]
\[ \frac{A}{B} = \frac{\tfrac{1}{2} - \tfrac{2}{5}}{\tfrac{4}{7} - \tfrac{1}{2}} = \frac{\tfrac{1}{10}}{\tfrac{1}{14}} = \frac{14}{10} = \frac{7}{5} \]
Vessel A is richer in milk and is further from the target than B, so it contributes the larger share - 7 parts to 5.
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