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 obtains an annual total interest of :

(A) Rs. 1800

(B) Rs. 2000

.:

Let us take that the trust invests Rs. x at 5\% p.a. and then the trust invests Rs. (30, 000$-$x) at 7\% p.a.

(A) So, [x 30,000$-$x] $\left[ {\begin{array}{cccccccccccccccccccc}{5\% }\\{7\% }\end{array}} \right]$ = 1800

$\Rightarrow$ $\cfrac{{5x}}{{100}}$+ (30, 000$-$ x) × $\cfrac{7}{{100}}$= 1800
$\Rightarrow$ 5x + 2,10,000$-$7x = 1,80,000

$\Rightarrow$ 2x = 2,10,000 $-$ 1,80,000
$\Rightarrow$ 2x = 30,000 $\Rightarrow$ x = 15,000

Hence, the trust invests Rs. 15,000 at 5\% p.a. and Rs. (30,000$-$x) = Rs. (30,000$-$15000)

= Rs. 15,000 at 7\% p.a.

(B) [x 30,000$-$ x]$\left[ {\begin{array}{cccccccccccccccccccc}{5\% }\\{7\% }\end{array}} \right] = 2000$
$\Rightarrow$ $x \times = \cfrac{5}{{100}}$+ (30, 000$-$x) × $\cfrac{7}{{100}}$= 2000

$\Rightarrow$ 5x + 2,10,000$-$7x = 200000

$\Rightarrow$ 2x = 2,10,000$-$2,00,000
$\Rightarrow$ 2x = 10,000 $\Rightarrow$ x = 5,000
Hence, the trust invests Rs. 5,000 at 5\% p.a. and Rs.(30,000$-$ 5,000) = Rs. 25,000 at 7\% p.a.