Question

A pen and a pencil cost $Rs.12$. Three pencils and five pens cost $Rs.56$. Find the cost of one pen and one pencil.

Answer 1

Let the cost of one pen and one pencil be $x,y$ respectively.
Since, we have
$x+y=12$ ……. (1)
$5x+3y=56$ ..….. (2)

On solving, from equations$\left(1\right)\times 5-\text{equation}\left(2\right)$, we get
$5x+5y=60$
$5x+3y=56$
$\underset{–}{---}$
$\Rightarrow 2y=4$
$\Rightarrow y=2$
Substitute $y=2$ in equation(1), we get
$\Rightarrow x+2=12$
$\Rightarrow x=12-2$
$\Rightarrow x=10$
Hence, the cost of one pen is $Rs10$ and one pencil is $Rs2$.