Question

A 90 kg solution has 10% salt. How much water must be evaporated to have the solution with 20% salt?

• A. 45 kg
• B. 30 kg
• C. 40 kg
• D. 45 kg

Hint:

When solving concentration problems, use the mass of solute and total mass, then solve for the unknown quantity based on the desired concentration.

Answer 1

The Correct Option is A

Step 1: The amount of salt in the solution initially is: \[ \text{Salt} = 10\% \times 90 = 9 \text{ kg} \] 
Step 2: Let the amount of water to be evaporated be \( x \) kg. After evaporation, the total mass of the solution will be \( 90 - x \) kg, and the amount of salt remains the same, i.e., 9 kg. 
Step 3: The new concentration of salt is 20\%, so: \[ \frac{9}{90 - x} = 20\% \] 
Step 4: Solve the equation: \[ \frac{9}{90 - x} = \frac{20}{100} \] \[ 9 \times 100 = 20 \times (90 - x) \] \[ 900 = 1800 - 20x \] \[ 20x = 900 \quad \implies \quad x = 45 \] Thus, 45 kg of water must be evaporated.