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

The Correct Option is A

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