Blending two sugar solutions: Two sugar solutions of 30% and 50% concentrations are mixed to obtain a 45% mixture. In what proportion should the two solutions be mixed (30% : 50%)?

Introduction / Context:
Alligation quickly gives the ratio in which two concentrations must be combined to reach a target concentration. Here we want 45% from 30% and 50%.

Given Data / Assumptions:

• Solutions: 30% and 50%.
• Target concentration = 45%.

Concept / Approach:
Alligation ratio (30% : 50%) = (50 − 45) : (45 − 30) = 5 : 15 = 1 : 3. This gives the required mixing proportion for 30% to 50% solution.

Step-by-Step Solution:
Difference on high side = 50 − 45 = 5.Difference on low side = 45 − 30 = 15.Therefore, 30% : 50% = 5 : 15 = 1 : 3.

Verification / Alternative check:
Test with 1 L of 30% and 3 L of 50%. Pure sugar = 0.3 + 1.5 = 1.8 in 4 L → 1.8/4 = 45% exactly.

Why Other Options Are Wrong:

• 3 : 1 would yield 35%, not 45%.
• 2 : 3 and 3 : 2 give other averages, not 45%.

Common Pitfalls:

• Swapping the alligation differences, which would invert the required ratio.

Final Answer:
1 : 3