After 25 kg of water had been evaporated from a solution of salt and water, which had 20% salt, the remaining solution had 30% salt. Find the weight of the original solution.
Answer
Answer (as printed):
Explanation
Let the weight of the original solution be $x$ kg. Then, weight of salt in $x$ kg solution $=20 \%$ of $x$ kg $=\frac{x}{5}$ kg. Weight of water in $x$ kg solution $=\left(x-\frac{x}{5}\right) \mathrm{kg}=\frac{4 x}{5} \mathrm{kg}$. Weight of solution after evaporation $=(x-25)$ kg. $\therefore \frac{x}{5(x-25)}=\frac{30}{100} \Leftrightarrow 150(x-25)=100 x \Leftrightarrow 50 x=3750 \Leftrightarrow x=75$. Hence, weight of the original solution $=75$ kg.