Two solids A and B float in water. It is observed that A floats with  12 of its body immersed in water and B floats with  14 of its volume above the water level. The ratio of the density of A to that of B is

The density of a substance is defined as its mass per unit volume. When an object floats, the volume of water displaced is equal to the volume of the object that is submerged. This is due to Archimedes' principle, which states that the buoyant force (the force that makes the object float) is equal to the weight of the fluid displaced by the object.

For solid A, 1/2 of its body is immersed in water. This means that it displaces a volume of water equal to 1/2 of its own volume. Since the density of the object is equal to the mass divided by the volume, and the mass of the water displaced is equal to the volume of water displaced times the density of water, we can say that the density of A is equal to 1/2 the density of water.

For solid B, 3/4 of its body is immersed in water (since 1/4 is above the water level). This means that it displaces a volume of water equal to 3/4 of its own volume. Using the same logic as above, we can say that the density of B is equal to 3/4 the density of water.

Therefore, the ratio of the density of A to that of B is (1/2) / (3/4) = 2/3.