Question

$37$ pens and $53$ pencils together cost Rs. $320$, while $53$ pens and $37$ pencils together cost Rs. $400$. Find the cost of a pen and that of a pencil.

Answer 1

Let the cost of a pen be $Rs.x$ and that of a pencil be $Rs.y$. Then,

$37x+53y=320$ .(i)

and, $53x+37y=400$ ..(ii)

Adding equations (i) and (ii), we get

$90x+90y=720\Rightarrow x+y=8$ ..(iii)

Substituting equation (i) and (ii), we get

$16x-16y=80\Rightarrow x-y=5$ ..(iv)

Adding equations (iii) and (iv), we get

$2x=13\Rightarrow x=6.5$

Substituting $x=6.5$ in equation (iii), we get

$y=(8-6.5)=1.5$

Hence, cost of one pen $=$ Rs. $6.50$ and cost of one pencil $=$Rs. $1.50$.