#### Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question 74 sub question (i)

Answer: Rs 15000 invested in the first bond and Rs 15000 invested in the second bond

Hint: Matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.

Given: Total amount to invest in 2 different types of bonds=Rs 30000

First bond pays 5% interest per year

Second bond pays 7% interest per year

Let Rs x can be invested in the first bond then, the sum of money invested in the second bond will be Rs (30000-x)

First bond pays 5% interest per year second bond pays 7% interest per year

$\therefore$ In order to obtain an annual total interest of Rs 1800, we have

$\Rightarrow[x \quad(30000-x)]\left[\begin{array}{c} \frac{5}{100} \\ \frac{7}{100} \end{array}\right]=1800\\$

$\therefore$ simple interest for 1 year

$=\frac{\text { principal } \times \text { rate }}{100}$

$\\ \Rightarrow \frac{5 x}{100}+\frac{7(30000-x)}{100}=1800\\\\ \Rightarrow 5 x+210000-7 x=180000\\\\ \Rightarrow 210000-2 x=180000\\\\ \Rightarrow 2 x=210000-180000\\\\ \Rightarrow 2 x=30000\\\\ \Rightarrow x=\frac{30000}{2}\\\\ \Rightarrow x=15000$

Thus, in order to obtain an annual total interest of Rs 1800, the trust should invest Rs 15000 in the first bond and the remaining Rs15000 in the second bond.