Henry Ernest Dudeney/Puzzles and Curious Problems/297 - Mixing the Wine/Solution

by : $297$

 * Mixing the Wine

Solution

 * $7$ parts wine to $17$ parts water.

Proof
Let $c$ be the capacity of one glass.

After they have been filled with water:
 * the first one contains $\dfrac {4 c} {12}$ of wine
 * the second one contains $\dfrac {3 c} {12}$ of wine.

In the jug together, there is $\dfrac {7 c} {12}$ of wine out of a total of $2 c$ of liquid.

When poured into one of the glasses, there is then $\dfrac 1 2 \times \dfrac {7 c} {12} = \dfrac {7 c} {24}$ of wine.

As this is in a container of capacity $c$, the ratio of wine to water is $\dfrac {7 c} {24} \div \dfrac {24 - 7 c} {24} = \dfrac 7 {17}$.