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Class 12 Determinants · Long Answer3 Marksmatrix_method_applications

Class 12 Maths · Determinants · Long Answer #56

A trust invests in two bonds paying 10% and 12% annual interest. Total interest is ₹2,800. Interchanging the invested amounts would reduce the interest by ₹100. Using matrices, find each investment.

✅ Step-by-Step Solution

Final Answer: ₹10,000 in the 10% bond; ₹15,000 in the 12% bond.
  1. Let investments be x,y. The equations 0.10x+0.12y=2800 and 0.12x+0.10y=2700 become [[10,12],[12,10]][x,y]ᵀ=[280000,270000]ᵀ.
  2. The coefficient determinant is 100−144=−44≠0; its inverse is (−1/44)[[10,−12],[−12,10]].
  3. Multiply that inverse by the right side to obtain (−1/44)[−440000,−660000]ᵀ=[10000,15000]ᵀ.
  4. The investments are ₹10,000 and ₹15,000 respectively; their interest totals verify ₹2,800 and ₹2,700 after interchange.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let investments be x,y. The equations 0.10x+0.12y=2800 and 0.12x+0.10y=2700 become [[10,12],[12,10]][x,y]ᵀ=[280000,270000]ᵀ.
  • [1 mark] The coefficient determinant is 100−144=−44≠0; its inverse is (−1/44)[[10,−12],[−12,10]].
  • [1 mark] Multiply that inverse by the right side to obtain (−1/44)[−440000,−660000]ᵀ=[10000,15000]ᵀ.
  • [0.5 marks] The investments are ₹10,000 and ₹15,000 respectively; their interest totals verify ₹2,800 and ₹2,700 after interchange.

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