# A trust fund has Rs 30000 that must be invested in two different types of bonds.

Question:

A trust fund has Rs 30000 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 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of
(i) Rs 1800 (ii) Rs 2000

Solution:

If Rs $x$ are invested in the first type of bond and Rs ( $30000-x$ ) are invested in the second type of bond, then the matrix $A=[x \quad 30000-x]$ represents investment and the matrix $B=\left[\begin{array}{l}\frac{5}{100} \\ \frac{7}{100}\end{array}\right]$ represents rate of interest.

(i)

$\left[\begin{array}{ll}x & 30000-x\end{array}\right]\left[\begin{array}{c}\frac{5}{100} \\ \frac{7}{100}\end{array}\right]=[1800]$

$\Rightarrow\left[\frac{5 x}{100}+\frac{7(30000-x)}{100}\right]=[1800]$

$\Rightarrow \frac{5 x+210000-7 x}{100}=1800$

$\Rightarrow 210000-2 x=180000$

$\Rightarrow 2 x=30000$

$\Rightarrow x=15000$

Thus,
Amount invested in the first bond = Rs 15000

Amount invested in the second bond $=$ Rs $(30000-15000)$

$=\mathrm{Rs} 15000$

(ii)

$\left[\begin{array}{ll}x & 30000-x\end{array}\right]\left[\begin{array}{c}\frac{5}{100} \\ \frac{7}{100}\end{array}\right]=[2000]$

$\Rightarrow\left[\frac{5 x}{100}+\frac{7(30000-x)}{100}\right]=[2000]$

$\Rightarrow \frac{5 x+210000-7 x}{100}=2000$

$\Rightarrow 210000-2 x=200000$

$\Rightarrow 2 x=10000$

$\Rightarrow x=5000$

Thus,
Amount invested in the first bond = Rs 5000

\begin{aligned} \text { Amount invested in the second bond } &=\text { Rs }(30000-5000) \\ &=\text { Rs } 25000 \end{aligned}