Question

$5$ pencils and $7$ pens together cost Rs. $50$ whereas $7$ pencils and $5$ pens together cost Rs. $46$. Find the sum of cost of one pencil and that of one pen.

Answer 1

Let cost(in RS) of one pencil $=x$ and cost (in RS) of one pen $=y$

Therefore , according to question

$5x+7y=50$ ........ $\left(1\right)$

$7x+5y=46$ ......... $\left(2\right)$

Multiply equation $\left(1\right)$ by $7$ and equation $\left(2\right)$ by $5$, we get

$7(5x+7y)=7\times 50$

$35x+49y=350$ ....... $\left(3\right)$

and

$5(7x+5y)=5\times 46$

$35x+25y=230$ ....... $\left(4\right)$

Subtract equation $\left(4\right)$ from equation $\left(3\right)$, we get

$35x+49y-35x-25y=350-230$

$49y-25y=120$

$24y=120$

$y=\frac{120}{24}$

$y=5$

Substitute $y=5$ in equation $\left(1\right)$, we get

$5x+7\times 5=50$

$5x+35=50$

$5x=50-35$

$5x=15$

$x=\frac{15}{5}$

$x=3$

Hence, Cost of One Pencil $=x=3$ and cost of One Pen $=y=5$