Question

A solution of salt and water contains $15\%$ salt by weight. $30$ kg of water evaporates and the solution now contains $20\%$ of the salt. The original quantity of the solution is

• A. $100$ kg
• B. $110$ kg
• C. $115$ kg
• D. $120$ kg

Answer 1

The correct option is D $120$ kg

Let the amount of water in the original solution $=x$ kg.

Then the amount of salt present in $15\%$ of this solution $=$ $\frac{15x}{100}kg=\frac{3x}{20}$ kg.

After $30$ kg water evaporates, the amount of water $=(x=30)$ kg.

So, the new concentration $=$ $\frac{\frac{3x}{20}}{x-30}\times 100$.

Then, by the given condition,

$\frac{\frac{3x}{20}}{x-30}\times 100=20$

$\Rightarrow 4x-120=3x$

$\Rightarrow x=120$ kg

So, the quantity of the original solution $=120$ kg.

So, option D is correct.