Tea-price alligation: In what proportion should teas priced at ₹ 62/kg and ₹ 72/kg be mixed to obtain a blend worth ₹ 65/kg?

Introduction / Context:
Alligation is a quick method to find the ratio of two ingredients to achieve a desired mean price or concentration. We apply it directly to per-kilogram prices here.

Given Data / Assumptions:

• Cheaper tea = ₹ 62/kg; dearer tea = ₹ 72/kg.
• Target blend price = ₹ 65/kg.

Concept / Approach:
Alligation ratio (cheaper : dearer) = (dearer − mean) : (mean − cheaper) = (72 − 65) : (65 − 62) = 7 : 3. Mix in this ratio by weight.

Step-by-Step Solution:
Compute differences: 72 − 65 = 7 and 65 − 62 = 3.Therefore, ratio cheaper : dearer = 7 : 3.

Verification / Alternative check:
Pick 7 kg of ₹ 62 and 3 kg of ₹ 72. Total cost = 7*62 + 3*72 = 434 + 216 = 650 for 10 kg → price per kg = ₹ 65, confirming the ratio.

Why Other Options Are Wrong:

• 4 : 6 reduces to 2 : 3 (not matching the computed 7 : 3).
• 2 : 3 and 4 : 7 do not yield ₹ 65/kg when tested.

Common Pitfalls:

• Reversing the differences leading to the inverse ratio.

Final Answer:
7 : 3