Evaporating a salt solution

Statement

From $80$ kg of a $4\%$ salt solution, how much water must be evaporated so that the solution becomes $10\%$ salt?

Solution

Mass of salt (constant). Evaporation removes only water, so the amount of salt does not change: $\text{salt} = 4\% \text{ of } 80 = 0.04 \cdot 80 = 3.2 \text{ kg}.$

New total mass. Call $T$ the final mass of the solution. The salt must be $10\%$ of it: $3.2 = 0.10 \cdot T \implies T = 32 \text{ kg}.$

Water evaporated. $80 - 32 = 48$ kg. Check: $\dfrac{3.2}{32} = 0.10 = 10\%$. Correct. $\boxed{48 \text{ kg of water}}$