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 Rs 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of (i) Rs 1800 (ii) 2000.

Answer

N/a

Explanation

Let the sum inverested in first bond =Rs. X
`therefore` sum inverested in second bond =Rs. (30000-x)
(a) [x30000-x] `-{:(5%),(7%):}]=[18000]`
`implies [(5x)/(100)+(7(30000-x))/(100)]=[1800]`
`implies (210000-2x)/(100)=[1800]`
`implies 210000-2x=180000`
`implies 2x=30000implies x=15000`
`therefore 30000-x=30000-15000=15000`
`implies ` the sum inverested in two bonds are Rs. 15000 and Rs. 15000 respectively.
`(B) [x" "30000-x][{:(5%),(7%):}]=[2000]`
`implies [(5x)/(100)+(7(30000-x))/(100)]=[2000]`
`implies 210000-2x)/(100
)=2000`
`implies 210000-2x=200000`
`implies 2x=10000`
`implies x=5000`
`therefore 30000-x=30000-5000`
`=25000`
`implies ` The sum inversted in two bonds are Rs. 5000 and RS. 25000 respectively.