A solid floats in a liquid at `20^@`C with 75 % of it immersed. When the liquid is heated to `100^@`C, the same solid floats with `80%` of it immersed in the liquid. Calculate the coefficient of expansion of the liquid. Assume the volume of the solid to be constant.

Explanation

To solve the problem, we need to analyze the conditions under which the solid floats in the liquid at two different temperatures and relate the densities of the liquid at those temperatures to find the coefficient of expansion of the liquid.

### Step-by-Step Solution:

1. **Understanding the Floating Condition**:
The buoyant force (Fb) acting on the solid must equal the weight of the solid (mg) for it to float. The buoyant force is given by:
\[
F_b = \text{density of liquid} \times g \times \text{volume immersed}
...