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CBSE Class 12 Mathematics 2026 Main Paper 65/5/2 · Q325 Marksmatrix_linear_systems

CBSE Class 12 Mathematics 2026 Main Paper 65/5/2 · Question 32 (Matrices)

Let a,b,c be prices per kg for three fertilizers. One kg each of A and C plus 2 kg of B costs ₹400. B and C together cost as much as A. Three kg of B plus ₹200 costs as much as A and C together. Use matrices to find the prices.

✅ Step-by-Step Solution

Final Answer: A ₹180/kg, B ₹40/kg and C ₹140/kg.
  1. Write the augmented matrix with rows (1,2,1 | 400),(1,−1,−1 | 0),(1,−3,1 | 200).
  2. Subtract row 3 from row 1 to get 5b=200, hence b=40.
  3. Then a+c=320 and a−c=40, so a=180 and c=140.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Write the augmented matrix with rows (1,2,1 | 400),(1,−1,−1 | 0),(1,−3,1 | 200).
  • [3 marks] Subtract row 3 from row 1 to get 5b=200, hence b=40.
  • [1 mark] Then a+c=320 and a−c=40, so a=180 and c=140.

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