Mercury is 13.6 times as dense as liquid water. What would be the reading of a water-filled barometer at normal atmospheric pressure, 760. mmHg?

Density = mass / volume

Because the dimensions of the barometer are the same for each case, we can compare the heights of the liquids instead of the volume.

ρ (mercury) = 13.6ρ (water)

mass (mercury) / 760 = 13.6 x mass (water) / Height (water)

Masses of the liquids will also be the same.

Height of water = 13.6 x 760

Height of water = 10,336 mm