Wine fraction after mixing two diluted glasses

Two identical glasses hold wine: one is filled to a third of its capacity and the other to a quarter. Each is topped up with water, and both are emptied into a jug. Half of the jug is then poured back into a single glass. What fraction of the liquid in that glass is wine?

$7/24$. With capacity $1$, the jug holds $\tfrac13+\tfrac14=\tfrac7{12}$ wine in $2$ units of liquid. The mixture is uniform, so any portion is $\tfrac{7}{24}$ wine.