Question

A trust fund has Rs $30,000$ that must be invested in two different types of bonds.
The first bond pays $5$% interest per year, and the second bond pays $7$% interest per year.
Using matrix multiplication, determine how to divide Rs $30,000$ among the two types of bonds.
If the trust fund must obtain an annual total interest of:
$A.$ Rs $1,800$
$B.$ Rs $2,000$

Answer 1

(a) Let Rs $x$ be invested in the first bond. Then, the sum of money invested in the second bond will be Rs$(30000 − x).$ It is given that the first bond pays $5$% interest per year and the second bond pays $7$ % interest per year. Therefore, in order to obtain an annual total interest of Rs $1800$, we have: $\begin{bmatrix}x&(30000-x)\end{bmatrix}\begin{bmatrix}\frac{5}{100}\\\\\frac{7}{100}\end{bmatrix}=1800$ $[$S.I for 1 year=$\frac{Principal*Rate}{100}]$
$\Rightarrow\frac{5x}{100}+\frac{7(30000-x)}{100}=1800$
$\Rightarrow$ $5x+210000-7x=180000$
$\Rightarrow$ $210000-2x=180000$
$\Rightarrow$ $2x=210000-180000$
$\Rightarrow$ $x=15000$

Thus, in order to obtain an annual total interest of Rs $1800$, the trust fund should invest
Rs 15000 in the first bond and the remaining Rs $15000$ in the second bond.

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(b) Let Rs $x$ be invested in the first bond. Then, the sum of money invested in the second bond will be Rs ($30000 − x$).
Therefore, in order to obtain an annual total interest of Rs $2000$, we have:
$\begin{bmatrix}x&(30000-x)\end{bmatrix}\begin{bmatrix}\frac{5}{100}\\\\\frac{7}{100}\end{bmatrix}=2000$
$\Rightarrow \frac{5x}{100}+\frac{7(30000-x)}{100}=2000$
$\Rightarrow$ $5x+210000-7x=200000$
$\Rightarrow$ $2x=210000-20000$
$\Rightarrow$ $x=5000$

Thus, in order to obtain an annual total interest of Rs $2000,$ the trust fund should invest Rs $5,000$ in the first bond and the remaining Rs $25000$ in the second bond.