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 R 30000 amoung the two types of bonds, if the trust fund must obtain an annual total interest of
(a) Rs 1800

(b) Rs 2000

Answer 1

Let the amount invested in first type of bonds is Rs x, then that invested in second type of bonds will be Rs (30000 -x).
According to given condition,
$[x30000-x]\left[\begin{array}{c}\frac{5}{100}\\ \frac{7}{100}\end{array}\right]=\left[1800\right]\Rightarrow [\frac{5x}{100}+\frac{(30000-x)7}{100}]=\left[1800\right]\Rightarrow \frac{5x+210000-7x}{100}=1800\Rightarrow 210000-2x=180000\Rightarrow 30000=2x\Rightarrow x=15000$
Hence, the amounts invested in the two types of bonds are respectively Rs 15000 and Rs (30000-15000)=Rs 15000.

Let the amount invested in first type of bonds is Rs x, then that invested in second type of bonds will be Rs (30000 -x).
According to the given condition, $[x30000-x]\left[\begin{array}{c}\frac{5}{100}\\ \frac{7}{100}\end{array}\right]=\left[2000\right]\Rightarrow [\frac{5x}{100}+\frac{(30000-x)7}{100}]=\left[2000\right]$
Hence, the amounts invested in two types of bonds are respectively Rs 5000 and Rs (30000-5000)=Rs 25000.