Answer :

Given: There are two types of bonds paying 10% and 12% as interest.


To find: the amount invested by the trust in both the bonds using given conditions


Let the amount invested in the first and second bond be x and y respectively.


In first case:


The rate of interest in first and second bond be 10% and 12 % respectively







In second case:


The amounted invested in both the bonds gets interchanged


So, the amount in first and second bond is y and x respectively


The rate of interest in first and second bond be 10% and 12 % respectively









To solve these equations and get values of x, y, we have:


AX = B where,




Now, check whether system has unique solution or not:



= 10 × 10 – 12 × 12


= 100 – 144


= -44



The system of the equation is consistent and have unique solution


AX = B


X = A-1 B


Formula used:














Thus,




X = A-1 B








Solutions of the equations are x = 10000, y = 15000


Hence, the amount invested in the first and second bond is 10000 and 15000 respectively


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