Teas priced at ₹ 126/kg and ₹ 135/kg are mixed with a third variety in the ratio 1 : 1 : 2. If the resulting mixture is worth ₹ 153/kg, what is the price per kg of the third variety?

Introduction / Context:
This is a weighted-average problem across three components. The average price equals the total cost divided by total quantity, weighted by the mixing ratio.

Given Data / Assumptions:

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

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

Step-by-Step Solution:
(126 + 135 + 2x) / 4 = 153. 126 + 135 + 2x = 612. 2x = 612 − 261 = 351. x = 351 / 2 = ₹ 175.5 per kg.

Verification / Alternative check:
Substitute back: total cost = 126 + 135 + 2*175.5 = 612; divide by 4 = 153. Correct.

Why Other Options Are Wrong:
Values like ₹ 170, ₹ 169.5, ₹ 180, ₹ 165 do not satisfy the weighted-average equation with ratio 1 : 1 : 2.

Common Pitfalls:
Averaging the prices arithmetically without weighting or miscounting the two parts of the third variety.

Final Answer:
₹ 175.5