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  • On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, every one would have got Rs 10 more. However, if there were 16 children more, every one would have got rs 10 less. Using matrix method,

On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, every one would have got Rs 10 more. However, if there were 16 children more, every one would have got rs 10 less. Using matrix method, find out the number of children and the amount distributed by Seema. What values are reflected by Seema's decision ?  

 

 

 

 
 
 
 
 

Answers (1)

Let the number of children be x and the amount distributed by Seema for one children be Rs y.

So (x-8)(y+10)=xy\Rightarrow 5x-4y=40\: \: \: (i)

and (x+16)(y-10)=xy\Rightarrow 5x-8y=-80\: \: \: (ii)

To solve (i) and (ii), Let  A=\begin{bmatrix} 5 &-4 \\ 5 & -8 \end{bmatrix} ,  B=\begin{bmatrix} 40\\-80 \end{bmatrix}

X=\begin{bmatrix} x\\y \end{bmatrix}    \because AX=B\Rightarrow X=A^{-1}B

Now,  A^{-1}=\frac{1}{-40+20}\begin{bmatrix} -8 &4 \\ -5 &5 \end{bmatrix}=\frac{1}{20}\begin{bmatrix} 8 &-4 \\ 5 &-5 \end{bmatrix}

\therefore X =\frac{1}{20}\begin{bmatrix} 8 &-4 \\ 5 &-5 \end{bmatrix}\begin{bmatrix} 40\\-80 \end{bmatrix}\Rightarrow \begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 32\\30 \end{bmatrix}

Clearly x=32,y=30

Hence the number of children = 32 and the amount distributed by Seema = Rs 30.

 

Posted by

Ravindra Pindel

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