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

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

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