A mixture contains spirit and water in the ratio 3:2 (spirit:water). If the mixture contains 3 litres more spirit than water, what is the quantity of spirit (in litres) in the mixture?

Introduction / Context:
This is a ratio-and-difference question. When two quantities are in a ratio, you can represent them as multiples of a common factor. The difference between the two quantities then becomes the difference in parts times that common factor. Since the difference is provided as a real number (3 litres), you can solve for the factor quickly and then compute the required component (spirit). This method is faster and clearer than trial and error.

Given Data / Assumptions:

• Spirit : Water = 3 : 2
• Spirit is 3 litres more than water
• Let common factor = k litres per part

Concept / Approach:
If spirit:water = 3:2, then spirit = 3k and water = 2k. The difference is 3k - 2k = k. Since the difference equals 3 litres, k = 3. Then spirit = 3k.

Step-by-Step Solution:
Let spirit = 3k and water = 2k Difference = 3k - 2k = k Given difference = 3 litres, so k = 3 Spirit = 3k = 3 * 3 = 9 litres

Verification / Alternative check:
If spirit is 9 litres, then water must be 6 litres to maintain the 3:2 ratio. The difference 9 - 6 = 3 litres, which matches the condition. Both ratio and difference are satisfied, so the solution is correct.

Why Other Options Are Wrong:
8 and 10 do not allow water to be exactly 3 litres less while keeping ratio 3:2. 12 would pair with water 9 giving ratio 4:3, not 3:2. 15 would pair with water 12 giving ratio 5:4, not 3:2.

Common Pitfalls:
Treating 3 litres as total mixture, not as the difference, or using 3/2 directly as a fraction without forming part variables.

Final Answer:
The quantity of spirit is 9 litres.