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  • A typist charges Rs 145 for typing 10 English and 3 Hindi pages, while charges for typing 3 English and 10 Hindi pages are Rs 180. Using matrices, find the charges of typing one English and one Hindi page separately. However typist charged only Rs

A typist charges Rs 145 for typing 10 English and 3 Hindi pages, while charges for typing 3 English and 10 Hindi pages are Rs 180. Using matrices, find the charges of typing one English and one Hindi page separately. However typist charged only Rs 2 per page from a poor student Shyam for 5 Hindi pages. How much less was charged from this poor boy? Which values are reflected in this problem?

 

 

 

 
 
 
 
 

Answers (1)

Let the charges of typing one English page be x and that of one Hindi page be Rs y.

So,  10x+3y=145\; \; \; -(i)  &  3x+10y=180\; \; \; -(ii)

To solve (i) and (ii), let  

A=\begin{bmatrix} 10 &3 \\ 3 &10 \end{bmatrix}  and  B=\begin{bmatrix} 145 \\ 180 \end{bmatrix}.

X=\begin{bmatrix} x \\ y \end{bmatrix}

\because AX=B\Rightarrow X=A^{-1}B

Now A^{-1}=\frac{1}{100-9}\begin{bmatrix} 10 &-3 \\ -3 &10 \end{bmatrix}=\frac{1}{91}\begin{bmatrix} 10 & -3\\ -3 & 10 \end{bmatrix}

X=\frac{1}{91}\begin{bmatrix} 10 & -3\\ -3 & 10 \end{bmatrix}\begin{bmatrix} 145\\ 180 \end{bmatrix}\Rightarrow \begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 10\\15 \end{bmatrix}

Clearly x=10,y=15

Hence, the charge of typing one English page is Rs 10 and that of one Hindi page is Rs 15. So, typing cost of 5 Hindi pages would be normally 75. But the poor boy was charged only Rs 10. Therefore the poor boy was Rs 65 less charged.

Value reflected : 

Helpfulness towards the poor and needy people.

Posted by

Ravindra Pindel

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