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 determine the volumes \( V_1 \) and \( V_2 \) of a body floating in two different liquids with different densities. Let's go through the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a body with density \( \rho \) and total volume \( V \).
- The body is partially submerged in two liquids: one with density \( \rho_1 \) and the other with density \( \rho_2 \) (where \( \rho_1 > \rho_2 \)).
- The volume submerged in liquid 1 is \( V_1 \) and in liquid 2 is \( V_2 \).
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