Alligation (Tea Prices): At what ratio should tea at ₹300/kg be mixed with tea at ₹200/kg to obtain a mixture costing ₹225/kg (ratio given as 300:200)?

Introduction / Context:Price alligation problems find the mixing proportion of costlier and cheaper grades for a desired mean price.

Given Data / Assumptions:

• Costlier = ₹300/kg, Cheaper = ₹200/kg.
• Mean price = ₹225/kg.

Concept / Approach:Alligation rule: quantity ratio (cheaper:dearer) = (dearer − mean) : (mean − cheaper) = (300 − 225) : (225 − 200) = 75 : 25 = 3 : 1. Question asks for 300:200 (dearer:cheaper); invert to 1 : 3.

Step-by-Step Solution:1) Compute differences from mean.2) Obtain cheaper:dearer = 3:1.3) Convert to asked order (300:200) ⇒ 1:3.

Verification / Alternative check:Weighted average with 1 part ₹300 and 3 parts ₹200: (1*300 + 3*200)/4 = (300 + 600)/4 = 900/4 = 225.

Why Other Options Are Wrong:3:1 or 4:1 would raise mean above ₹225; 1:4 would lower it below ₹225.

Common Pitfalls:Reporting the ratio in the wrong order (cheaper:dearer instead of dearer:cheaper).

Final Answer:1 : 3