100 mL of a mixture of methanol (boiling point 338 K) and water (373 K) is distilled…

Step 1. (a) Methanol, the liquid with the lower boiling point. While it is boiling off, the thermometer stays at its boiling point.

Step 2. (b) $35\ \text{mL}$ came over at $338\ \text{K}$, out of $100\ \text{mL}$: $\dfrac{35\ \text{mL}}{100\ \text{mL}} \times 100 = 35\ \%$.

Why it rises. When the methanol is gone, only water is left, and the thermometer climbs to the boiling point of water.