In what ratio should water be added to spirit so that selling the resulting mixture at the cost price of spirit yields a 25% gain?

Introduction / Context: Water is free; spirit has cost. If the mixture is sold at the cost price of spirit, the only source of profit is the added water. A 25% gain means the water amount is one-quarter of the spirit content in the mixture.

Given Data / Assumptions:

• Selling price equals cost price of spirit.
• Profit% = (water quantity / spirit quantity) * 100.
• Desired profit = 25%.

Concept / Approach: Set water/spirit = 25/100 = 1/4. Then express the mixing ratio (water : spirit) accordingly. This directly gives the answer without additional algebra.

Step-by-Step Solution: Let spirit = 4 units (paid component). To gain 25%, water must be 1 unit so that profit = 1/4 of spirit cost. Therefore, ratio water : spirit = 1 : 4.

Verification / Alternative check: Sell 5 units (4 paid + 1 free) at the cost of 4 units. Revenue equals the cost of 4 units; the extra 1 unit creates a 25% gain on the cost outlay of spirit.

Why Other Options Are Wrong: 4 : 1 and others imply far more water or the wrong proportion, leading to different profit percentages.

Common Pitfalls: Confusing profit% with water% in the mixture. The 25% gain relates to water compared to spirit, not to the total mixture.

Final Answer: 1 : 4