Question
A trust fund of ₹30000 is invested in two bonds: 5% and 7%. Find the investment in each bond if total annual interest is: (i) ₹1800 (ii) ₹2000
Solution
Step 1: Let Variables
\[ x = \text{amount at 5%}, \quad y = \text{amount at 7%} \]Step 2: Form Equations
\[ x + y = 30000 \] \[ 0.05x + 0.07y = I \](i) When Interest = ₹1800
\[
0.05x + 0.07y = 1800
\]
Multiply by 100:
\[
5x + 7y = 180000
\]
Matrix Form
\[ \begin{bmatrix} 1 & 1 \\ 5 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 30000 \\ 180000 \end{bmatrix} \]Solution
\[ y = 15000,\quad x = 15000 \]Answer
₹15000 at 5% and ₹15000 at 7%
(ii) When Interest = ₹2000
\[
0.05x + 0.07y = 2000
\]
Multiply by 100:
\[
5x + 7y = 200000
\]
Matrix Form
\[ \begin{bmatrix} 1 & 1 \\ 5 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 30000 \\ 200000 \end{bmatrix} \]Solution
\[ y = 25000,\quad x = 5000 \]Answer
₹5000 at 5% and ₹25000 at 7%