Discussion
Chaman has two big cans of wine and water mixture. Chaman mixes the contents of both the cans in a big container. The new mixture has half water and half wine. In what quantity did Chaman mix contents of Can 1 and 2 if Can 2 has wine to water ratio of 2:3 and Can 1 has wine to water ratio 5:3?
Answer: B
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 wine in each can.
\[ \text{Can 1} = \frac{5}{8} = 0.625, \qquad \text{Can 2} = \frac{2}{5} = 0.4, \qquad \text{mixture} = 0.5 \]
\[ \frac{\text{Can 2}}{\text{Can 1}} = \frac{0.625 - 0.5}{0.5 - 0.4} = \frac{0.125}{0.1} = \frac{5}{4} \]
So Can 1 : Can 2 \( = 4 : 5 \). The can further from the target proportion contributes less, which is why the weaker Can 2 is used in greater quantity.
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