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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