Let Rs30,000 be divided into two parts ,Assume one bond as x,then second one is Rs(30,000-x).Let us represent this by $1\times 2$ matrix.[x(30000-x)]

Given Rate of interest as 0.05&0.07 per rupee.Let us denote with matrix R of order $2\times 1$

$R=\begin{bmatrix}0.05\\0.07\end{bmatrix}$

$(i)\begin{bmatrix}x & 30000-x\end{bmatrix}\begin{bmatrix}0.05\\0.07\end{bmatrix}$

$\Rightarrow \begin{bmatrix}x\times (0.05)+(30000-x)\times 0.07\end{bmatrix}=1800$

$\frac{5x}{100}+\frac{7(30000-x)}{100}=1800$

Multiplying by 100

5x+210000-7x=180000

2x=210000-180000=30000

x=15000

$\Rightarrow 30-x=30000-15000=15000.$

Thus the two part are 15000 each.

(ii)Given total interest 2000

$\begin{bmatrix}x & 30000-x\end{bmatrix}\begin{bmatrix}0.05\\0.07\end{bmatrix}=2000$

$\frac{5x}{100}+\frac{7(30000-x)}{100}=2000$

Multiplying by 100 on both sides

5x+210000-7x=200000

2x=210000-200000

x=5000

30000-x=30000-5000=25000

Thus the two parts are 25000&5000.