Tea at Rs. 126/kg and Rs. 135/kg is mixed with a third variety in the ratio 1 : 1 : 2. If the mixture costs Rs. 153/kg, what is the price of the third variety?

Problem restatementThree teas priced at 126, 135, and x rupees per kg are mixed in the ratio 1 : 1 : 2 to yield Rs. 153/kg. Find x.

Given data

• Weights: 1, 1, and 2 parts.
• Mean price of mixture = Rs. 153/kg.

Concept/ApproachUse weighted average: (sum of price × parts) / total parts = mixture price.

Step-by-step calculation (126 + 135 + 2x) ÷ 4 = 153 261 + 2x = 612 ⇒ 2x = 351 ⇒ x = 175.5

Verification/AlternativePlug back: (126 + 135 + 2×175.5)/4 = (261 + 351)/4 = 612/4 = 153 (exact).

Common pitfalls

• Using 1 : 1 : 1 or averaging the three prices without weighting.

Final AnswerRs. 175.50 per kg