What will the mass fraction of salt become when adding 100 g of water to a solution weighing 200 g

What will the mass fraction of salt become when adding 100 g of water to a solution weighing 200 g with a mass fraction of salt of 12%

Mass fraction of solute w = m (r.v.) / m (solution), where m (solution) is the mass of the solution. We learn from here the mass of the solute m (r.v.) = w * m (r-ra).
When water is added, the mass of the solute will not change, and the mass of the new solution m (new solution) = m (solution) + m (water), where m (water) is the mass of added water.
We derive the general formula for the new mass fraction of salt w (new) = m (r.v.) / m (new r-ra)
w (new) = w * m (solution) / (m (solution) + m (water)) = 0.12 * 200 / (100 + 200) = 0.08 or 8%