Which measurable quantity remains the same when a liquid is transferred between containers?

The correct option is: Volume of the liquid remains unchanged.

To understand why this is the correct answer, let us break down the properties of liquids and analyze how they behave when transferred from one container to another:

1. Definite Volume: A liquid has a fixed or definite volume. This is because the molecules in a liquid are closely packed together by intermolecular forces, meaning they cannot easily compress or expand to fill a different amount of space. Therefore, if you transfer 50 milliliters of water from a tall glass to a wide bowl, the amount of space it occupies remains exactly 50 milliliters. The volume does not change.

2. Indefinite Shape: Unlike solids, liquids do not have a fixed shape. Because the particles in a liquid can slide past one another, a liquid will always flow and take the shape of whichever container it is placed in. Hence, the shape changes, making "Shape of the liquid remains unchanged" incorrect.

3. Mass and Density: The mass of a liquid is the amount of matter in it, which remains constant (it does not become zero, so "Mass of the liquid becomes zero" is incorrect). Since density is defined as mass divided by volume ($d=\frac{m}{V}$), and both mass and volume remain constant at a constant temperature, the density also remains constant (it does not increase, making "Density of the liquid always increases" incorrect).

Thus, the only quantity among the options that is preserved and remains the same is the volume of the liquid.