Question
A trust invested money in two bonds: 10% and 12%. Total interest = ₹2800 If investments are interchanged, interest becomes ₹2700. Find the investment using matrix method.
Solution
Step 1: Let
\[ x = \text{amount at 10%}, \quad y = \text{amount at 12%} \]Step 2: Form Equations
\[ 0.10x + 0.12y = 2800 \] \[ 0.12x + 0.10y = 2700 \]Step 3: Multiply by 100
\[ 10x + 12y = 280000 \] \[ 12x + 10y = 270000 \]Step 4: Matrix Form
\[ \begin{bmatrix} 10 & 12 \\ 12 & 10 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 280000 \\ 270000 \end{bmatrix} \]Step 5: Solve
\[ x = 12500,\quad y = 12500 \]Final Answer
Investment in 10% bond = ₹12500
Investment in 12% bond = ₹12500