To 200 g of a 20% soda solution, 200 ml of water and 50 g of soda were added. Find the mass fraction of the new solution.

m1 (soda) = ω1 (soda) * m1 solution (soda) / 100% = 20% * 200/100% = 40 g;
m (water) = ρ (water) * V (water) = 1 * 200 = 200 g;
m2 solution (soda) = m2 (soda) + m (water) = 50 + 200 = 250;
m3 (soda) = m1 (soda) + m1 (soda) = 40 + 50 = 90 g;
m3 solution (soda) = m1 solution (soda) + m2 solution (soda) = 200 + 250 = 450 g;
ω3 (soda) = m3 (soda) * 100% / m3 solution (soda) = 90 * 100% / 450 = 20%.