A body of density `rho` floats with volume `V_(1)` of its total volume `V` immersed in a liquid of density `rho_(1)` and with the remainder of volume `V_(2)` immersed in another liquid of density `rho_(2)` where `rho_(1)gtrho_(2)`. Find the volume immersed in two liquids. (`V_(1)` and `V_(2)`).

Explanation

To solve the problem, we need to analyze the forces acting on the floating body and apply the principle of buoyancy. Here's a step-by-step solution:

### Step 1: Understand the forces acting on the body
The body experiences two main forces:
1. The weight of the body acting downwards, which is given by:
\[ W = \rho V g \]
...