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,
You need to login to perform this action.
You will be redirected in
3 sec