The cost of 5 pens and 8 pencils together cost Rs. 120 while 8 pens and 5 pencils together cost Rs. 153 . Find the cost of a 1 pen and that of a 1 pencil.

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The cost of 5 pens and 8 pencils together cost Rs. 120 while 8 pens and 5 pencils together cost Rs. 153 . Find the cost of a 1 pen and that of a 1 pencil.

Solution:

Suppose the cost of 1 pen and 1 pencil are Rs. $x$ and Rs. $y$ respectively.
Then according to the question
$\begin{array}{ll} 5 x+8 y=120 \ldots \ldots \text { (i) } \\ 8 x+5 y=153 \ldots \ldots \text {.(ii) } \end{array}$
Adding equation(i) and equation(ii), we obtain
$\begin{array}{l} 13 x+13 y=273 \\ \Rightarrow x+y=21\dots \dots(iii) \end{array}$
Subtracting equation(i) from equation(ii), we obtain
$\begin{array}{l} 3 x-3 y=33 \\ \Rightarrow x-y=11\dots \dots(iv) \end{array}$
Now, adding equation(iii) and equation(iv), we obtain
$2 x=32 \Rightarrow x=16$
Substituting $\mathrm{x}=16$ in equation(iii), we get
$16+y=21 \Rightarrow y=5$
As a result, the cost of 1 pen and 1 pencil are respectively Rs.16 and Rs.5.