Tea alligation with three varieties: Tea priced at ₹ 126/kg and ₹ 135/kg are mixed with a third variety in the ratio 1 : 1 : 2. If the final mixture is worth ₹ 153/kg, find the price per kg of the third variety.

Introduction / Context: When three price points are mixed in a fixed quantity ratio, the overall price is the weighted average. Here, the third variety has an unknown price that must make the average equal to ₹ 153/kg across four equal parts (1 + 1 + 2).

Given Data / Assumptions:

• Prices: ₹ 126, ₹ 135, and ₹ x (unknown).
• Mix ratio: 1 : 1 : 2 (total parts = 4).
• Mixture price = ₹ 153/kg.

Concept / Approach: Use weighted average: (126*1 + 135*1 + x*2) / 4 = 153. Solve for x to get the third variety’s price per kilogram.

Step-by-Step Solution:

Verification / Alternative check: Substitute x = 175.50: (126 + 135 + 351) / 4 = 612 / 4 = 153, exactly as required.

Why Other Options Are Wrong: Values like ₹ 170 or ₹ 180 shift the weighted average below or above ₹ 153; only ₹ 175.50 balances the 1 : 1 : 2 mix.

Common Pitfalls: Taking a simple average of the three prices instead of a weighted average according to 1 : 1 : 2.

Final Answer: ₹ 175.50