Water (cost Rs. 0) is mixed with wine priced at Rs. 22.50 per liter to reduce the price to Rs. 18 per liter. In what proportion should water and wine be mixed (water : wine)?

Introduction / Context:
Water has zero cost. Mixing water with wine reduces the average price. Alligation directly gives the water-to-wine ratio to hit the target price of Rs. 18 per liter.

Given Data / Assumptions:

• Cheaper (water) = Rs. 0.
• Dearer (wine) = Rs. 22.50.
• Mean (mixture) = Rs. 18.

Concept / Approach:
By alligation: quantities are proportional to the differences from the mean. Water : Wine = (22.50 − 18) : (18 − 0).

Step-by-Step Solution:
Water : Wine = 4.5 : 18 = 1 : 4

Verification / Alternative check:
Take 1 L water and 4 L wine → total 5 L, total cost = 4*22.5 = 90; price per liter = 90/5 = 18.

Why Other Options Are Wrong:
Other ratios produce means higher or lower than 18; only 1 : 4 matches the target.

Common Pitfalls:
Mixing up water : wine with wine : water, or using direct instead of inverse differences.

Final Answer:
1 : 4