Answer
Verified
396.6k+ views
Hint:Assume investment on one of the bonds as a variable. Then you automatically get the investment on the second bond. After that form two matrices one for investments and one for interests per year. At last, get the annual interest and equate it to the value given in the question.
Complete step-by-step answer:
Let the investment on first bond be Rs $x$
Total investment$ = $Rs$30,000$
Investment on second bond$ = $Rs$\left( {30,000 - x} \right)$
Now let us represent investment per bond by the matrix $A$
$A = \left[ {\begin{array}{*{20}{c}}
x \\
{30000 - x}
\end{array}} \right]$
$A$ is a $2 \times 1$ matrix which means it has $2$ rows and $1$ columns.
Now we will represent interest per year by a matrix.
Interest paid by the first bond$ = 5\% $
Interest paid by the second bond$ = 7\% $.
$B = \left[ {\begin{array}{*{20}{c}}
{5\% }&{7\% }
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
{\dfrac{5}{{100}}}&{\dfrac{7}{{100}}}
\end{array}} \right]$
$B$ is the $1 \times 2$ matrix which means it has $1$ row and 2 columns.
Now the question arises why we took $B$ as the $1 \times 2$ matrix and not $2 \times 1$ like $A$
This answer is to the fact that matrix multiplication takes place only when the number of columns of the first matrix is equal to the number of rows of the second matrix.
As it is said that we have to solve it by matrix multiplication, therefore it is necessary to take the order of matrices $A$ and $B$ in such a way that matrix multiplication is possible.
Now total annual interest$ = $ interest per bond $ \times $ investment per bond
$1800 = {\left[ {\begin{array}{*{20}{c}}
{\dfrac{5}{{100}}}&{\dfrac{7}{{100}}}
\end{array}} \right]_{1 \times 2}} \times {\left[ {\begin{array}{*{20}{c}}
x \\
{30000 - x}
\end{array}} \right]_{2 \times 1}}$
$ = {\left[ {\dfrac{{5x}}{{100}} + \dfrac{7}{{100}}\left( {30000 - x} \right)} \right]_{1 \times 1}}$
$ = \dfrac{{5x + 21000 - 7x}}{{100}}$
$180000 = 210000 - 2x$
$2x = 30000$
$x = 15000$
Hence amount invested at $5\% = $ Rs$15000$
Amount invested at $7\% =$Rs$\left( {30,000 - x} \right)$= $ Rs$15000
Note:The most important part about this question is to choose the order of the matrix for matrix multiplication. Students choose the wrong order of the matrix and are not able to multiply the matrices or multiply them in the wrong way.
Also it should be known to you that:
Total annual interest $ = $ Interest $ \times $ investment.
Complete step-by-step answer:
Let the investment on first bond be Rs $x$
Total investment$ = $Rs$30,000$
Investment on second bond$ = $Rs$\left( {30,000 - x} \right)$
Now let us represent investment per bond by the matrix $A$
$A = \left[ {\begin{array}{*{20}{c}}
x \\
{30000 - x}
\end{array}} \right]$
$A$ is a $2 \times 1$ matrix which means it has $2$ rows and $1$ columns.
Now we will represent interest per year by a matrix.
Interest paid by the first bond$ = 5\% $
Interest paid by the second bond$ = 7\% $.
$B = \left[ {\begin{array}{*{20}{c}}
{5\% }&{7\% }
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
{\dfrac{5}{{100}}}&{\dfrac{7}{{100}}}
\end{array}} \right]$
$B$ is the $1 \times 2$ matrix which means it has $1$ row and 2 columns.
Now the question arises why we took $B$ as the $1 \times 2$ matrix and not $2 \times 1$ like $A$
This answer is to the fact that matrix multiplication takes place only when the number of columns of the first matrix is equal to the number of rows of the second matrix.
As it is said that we have to solve it by matrix multiplication, therefore it is necessary to take the order of matrices $A$ and $B$ in such a way that matrix multiplication is possible.
Now total annual interest$ = $ interest per bond $ \times $ investment per bond
$1800 = {\left[ {\begin{array}{*{20}{c}}
{\dfrac{5}{{100}}}&{\dfrac{7}{{100}}}
\end{array}} \right]_{1 \times 2}} \times {\left[ {\begin{array}{*{20}{c}}
x \\
{30000 - x}
\end{array}} \right]_{2 \times 1}}$
$ = {\left[ {\dfrac{{5x}}{{100}} + \dfrac{7}{{100}}\left( {30000 - x} \right)} \right]_{1 \times 1}}$
$ = \dfrac{{5x + 21000 - 7x}}{{100}}$
$180000 = 210000 - 2x$
$2x = 30000$
$x = 15000$
Hence amount invested at $5\% = $ Rs$15000$
Amount invested at $7\% =$Rs$\left( {30,000 - x} \right)$= $ Rs$15000
Note:The most important part about this question is to choose the order of the matrix for matrix multiplication. Students choose the wrong order of the matrix and are not able to multiply the matrices or multiply them in the wrong way.
Also it should be known to you that:
Total annual interest $ = $ Interest $ \times $ investment.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE