Question

How many kg of pure salt must be added to 30 kg of a 2% solution of salt and water to increase it to a 10% solution?

• A. $2\frac{2}{3}$ kg
• B. 15 kg
• C. 3 kg
• D. 14 kg

Answer 1

Answer: (A)

$2\frac{2}{3}$ kg

Answer 2

Let $x$ be the amount of pure salt to be added.
Initial salt in the solution $30 \, \text{kg} \times 2\% = 0.6 \, \text{kg}$
Final salt in the solution $0.6 + x \, \text{kg}$ of salt after adding $x$ kg of pure salt.
Final total weight $30 + x \, \text{kg}$
Now,
For a 10% solution

\Rightarrow\;$$\frac{0.6 + x}{30 + x} = 0.10
\Rightarrow\;$$0.6 + x = 0.10(30 + x)
\Rightarrow\;$$0.6 + x = 3 + 0.10x
\Rightarrow\;$$0.90x = 2.4
$\Rightarrow\;$ $x = \frac{2.4}{0.90} = 2.67 \, \text{kg}$

The correct option is (A): $2\frac{2}{3}$ or $2.67$ kg