Question

$5$ pencils and $7$ pens together costs Rs. $50$ whereas $7$ pencils and $5$ pens together costs Rs. $46$. Thus the cost of one pencil and one pen respectively is:

• A. Rs. $5$, Rs. $3$
• B. Rs. $3$, Rs. $5$
• C. Rs. $4$, Rs. $4$
• D. Rs. $2$, Rs. $6$

Answer 1

Answer: (B)

Rs. $3$, Rs. $5$

Let the cost of one pencil be Rs. $x$ and the cost of one pen be Rs. $y$
According to the first condition
$5x+7y=\mathrm{50....}eq\left(1\right)$
$\Rightarrow x=\frac{50-7y}{5}$
According to the second condition
$7x+5y=\mathrm{46....}eq\left(2\right)$
Put the value of $x$ in $eq\left(2\right)$
$\Rightarrow \frac{7(50-7y)}{5}+5y=46$
$\Rightarrow 350-49y+25y=230\Rightarrow y=5$

Resubstitute the value of $y$ to find the value of $x$
$\Rightarrow x=\frac{50-7\left(5\right)}{5}=\frac{50-35}{5}\Rightarrow x=3$
$\therefore$ cost of one pencil $=$ Rs. $3$ and cost of one pen $=$ Rs. $5$