Question

$5$ pencils and $7$ pens together cost Rs. $50$, whereas $7$ pencils and $5$ pens together cost Rs. $46$. The cost of one pencil is _____

• A. Rs. $8$
• B. Rs. $6$
• C. Rs. $3$
• D. Rs. $2$

Answer 1

Answer: (C)

Rs. $3$

Let $x$ represent the cost of one pencils and $y$ represent the cost of one pen. Then,

$5x+7y=50...\left(i\right)$
$7x+5y=46...\left(ii\right)$

From equation$\left(i\right)\times 7$equation $\left(ii\right)\times 5$ gives

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

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

Subtracting $\left(iv\right)$ from $\left(iii\right)$
$35x+49y-35x-25y=350-230$
$\Rightarrow 24y=120$
$\therefore y=5$

Substituting $y=5$ in $\left(i\right)$, we get $5x+7\left(5\right)=50$
$\Rightarrow 5x+35=50$
$5x=15$
$\therefore x=3$
Hence, the cost of one pencil is Rs. $3$