A body weighed on unequal beam scales is balanced with a 2 kg weight, if we put it on one scale pan, and a 3 kg weight

A body weighed on unequal beam scales is balanced with a 2 kg weight, if we put it on one scale pan, and a 3 kg weight, if we put it on the other. What is the body weight and what is the ratio of the lengths of the balance beams?

Let’s compose a system of equations based on the equality of moments:
x * L₁ = 2 * L₂;
3 * L₁ = x * L₂;
x = 2 * L₂ / L₁;
x = 3 * L₁ / L₂;
2 * L₂ / L₁ = 3 * L₁ / L₂;
L₂² / L₁² = 3/2.
now we need to find x:
x = 2 * √1.5 = √6 kg ≈ 2.45 kg;
Thus, we get:
L₂ / L₁ = √1.5.
Answer: √1.5.