After 30 kg of water had been evaporated from a solution of salt and water, which had 15% salt, the remaining solution had 20% salt. The weight of the original solution was

### Concept & Logic When water evaporates from a saltwater solution, the water content decreases, but the absolute amount of salt remains strictly constant. Setting up an equation based on this **Constant Component** solves the problem reliably. $$ \text{Initial Mass of Salt} = \text{Final Mass of Salt} $$ ### Step-by-Step Solution * **Given:** * Water evaporated = $30$ kg * Initial salt percentage = $15\%$ * Final salt percentage = $20\%$ * **Calculation:** * Let the original weight of the solution be $x$ kg. * The absolute mass of salt initially is $15\%$ of $x = 0.15x$. * After $30$ kg of water evaporates, the new weight of the solution becomes $(x - 30)$ kg. * The mass of salt in the new solution is $20\%$ of $(x - 30) = 0.20(x - 30)$. * Equating the constant salt mass: $0.15x = 0.20(x - 30)$. * Expand the right side: $0.15x = 0.20x - 6$. * Rearrange terms: $0.20x - 0.15x = 6$. * $0.05x = 6$. * $x = \frac{6}{0.05} = 120$ kg. ### Exam Strategy & Shortcut **Inverse Ratio Method:** Focus entirely on the constant component (salt). Its concentration increases from $15\%$ to $20\%$. This is a ratio of $15 : 20$, which simplifies to $3 : 4$. Because the absolute mass of salt is constant, the total volume of the solution must be inversely proportional, changing in the ratio of $4 : 3$. This means the volume dropped from $4$ parts to $3$ parts. The difference ($1$ part) represents the $30$ kg of evaporated water. If $1$ part $= 30$ kg, the original weight ($4$ parts) $= 4 \times 30 = 120$ kg. Solved in 10 seconds! ### Common Pitfall A frequent trap is trying to calculate the water percentage ($85\%$ initially, $80\%$ finally) and setting up an equation with those. Since the water amount is changing, this complicates the algebra unnecessarily and often leads to simple arithmetic mistakes. Always anchor to the unchanging element. ### Final Answer **Therefore, the correct answer is 120 kg.**