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
(a)80 kg
(b)90 kg
(c)120 kg
(d)135 kg
Answer
Answer (as printed): C
Explanation
Let the weight of the original solution be $x \mathrm{kg}$. Weight of salt in $x \mathrm{kg}$ of solution $=15 \%$ of $x \mathrm{kg}=\frac{3 x}{20} \mathrm{kg}$. $$\begin{aligned} \therefore \frac{\frac{3 x}{20}}{(x-30)}=\frac{20}{100} & \Rightarrow \frac{3 x}{20(x-30)}=\frac{1}{5} \\ & \Rightarrow 15 x=20(x-30) \Rightarrow 15 x=20 x-600 \\ & \Rightarrow 5 x=600 \Rightarrow x=120 \end{aligned}$$