Question

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 separtely. 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?

Answer 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) and 3x + 10y = 180 ...... (ii)

To solve (i) and (ii), let A = $\left(\begin{array}{cc}103& \\ 310& \end{array}\right)$, B = $\left(\begin{array}{cc}145& \\ 180& \end{array}\right)$, X = $\left(\begin{array}{cc}x& \\ y& \end{array}\right)$

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

Now $A^{-1}=\frac{1}{100-9}\left(\begin{array}{cc}103& \\ -310& \end{array}\right)=\frac{1}{91}\left(\begin{array}{cc}10-3& \\ -310& \end{array}\right)$ $\therefore X=\frac{1}{91}\left(\begin{array}{cc}10-3& \\ -310& \end{array}\right)\left(\begin{array}{cc}145& \\ 180& \end{array}\right)\Rightarrow \left(\begin{array}{cc}x& \\ y& \end{array}\right)=\left(\begin{array}{cc}10& \\ 15& \end{array}\right)$

Clearly x = 10, y = 15.

Hence the charge of typing one English page is Rs. 10 and that of one Hindi page be Rs. 15.

So, typing cost of 5 Hindi pages would be normally Rs. 75.

But the poor boy was charged only Rs. 10. Therefore, the poor boy was charged Rs. 65 less.

Value reflected : Helpfulness towards the poor and needy people.