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 2000

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Solution

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, $[x 30000 - x] ⎡ ⎣ \begin{matrix} \frac{5}{100} \frac{7}{100} \end{matrix} ⎤ ⎦ = [2000] \Rightarrow [\frac{5 x}{100} + \frac{(30000 - x) 7}{100}] = [2000]$
Hence, the amounts invested in two types of bonds are respectively Rs 5000 and Rs (30000-5000)=Rs 25000.

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