question_answer

A trust fund has Rs. 30000 is to be invested in two different types of bonds. The first bond pays 9% interest per annum which will be given to orphanage and second bond pays 11% interest per annum which will be given to an NGO cancer aid society. Using matrix multiplication, determine how to divide Rs. 30000 among two types of bonds, if the trust fund obtains an annual total interest of Rs. 3060? What are the values reflected in the question?        

Answer:

Let the two parts of Rs. 30000 be Rs. x and Rs. \[Rs.(30000-x);\] Respectively. Again, let A be \[1\times 2\] matrix representing these two parts. i.e.        \[\begin{align}   & \begin{matrix}    \text{Part}\,\,\text{I} & \text{Part}\,\,\text{II}  \\ \end{matrix} \\  & A=[\begin{matrix}    x & \,\,\,\,\,\,\,\,30000-x  \\ \end{matrix}] \\ \end{align}\] and R denotes \[2\times 1\] matrix representing the annual interest rate on two parts. i.e.        \[\begin{align}   & \begin{matrix}    \text{Part}\,\,\text{I} & \text{Part}\,\,\text{II}  \\ \end{matrix} \\  & A=[\begin{matrix}    0.09 & \,\,\,\,\,\,\,0.11  \\ \end{matrix}] \\ \end{align}\] Now, the total annual interest on the two parts is given by the matrix AR. i.e.        AR = 3060 \[\Rightarrow \]   \[[\begin{matrix}    x & 30000-x  \\ \end{matrix}]\,\,\left[ \begin{matrix}    0.09  \\    0.11  \\ \end{matrix} \right]=3060\] \[\Rightarrow \]   \[0.09x+0.11(30000-x)=3060\] \[\Rightarrow \]   \[\frac{9}{100}x+\frac{11}{100}(30000-x)=3060\] \[\Rightarrow \]   \[9x+330000-11x=306000\] \[\Rightarrow \]   \[2x=24000\] \[\Rightarrow \]   x = 12000 Hence, the required two parts of Rs. 30000 are Rs. 12000 and Rs. 18000, respectively                       Values (i) Charity. (ii) Helping orphans or poor people. (iii) Awareness about diseases,