Raising water percentage by adding water: A 20-kg mixture of spirit and water contains 10% water. How much water must be added so that water becomes 25% of the new mixture?

Introduction / Context: Increasing the percentage of a component by adding more of that component is a classic proportion problem. Track absolute water mass before and after the addition and form a single equation in the unknown added water.

Given Data / Assumptions:

• Total initial mixture = 20 kg with 10% water ⇒ 2 kg water, 18 kg spirit.
• Add w kg of water to reach 25% water in the new total.

Concept / Approach: New water mass = 2 + w. New total mass = 20 + w. Target fraction = (2 + w)/(20 + w) = 0.25. Solve for w.

Step-by-Step Solution:

Verification / Alternative check: New mixture = 24 kg with water = 6 kg ⇒ 6/24 = 25%, as required.

Why Other Options Are Wrong: 5 kg or 8 kg change the final water percentage to values other than 25%; 30 kg is far too large; 2 kg only raises water to 4/22 ≈ 18.18%.

Common Pitfalls: Treating percentages additively rather than using the ratio of new water to new total mass.

Final Answer: 4 kg