Question

The cost of $2$ pens and one pencil is Rs. $35$. The cost of $3$ pens and $4$ pencils is Rs. $65$. What is the cost of one pen?

• A. $20$
• B. $30$
• C. $15$
• D. $35$

Answer 1

Answer: (C)

$15$

Solution:- (C) $15$

Let the cost of pen and pencil be x and y

cost of $2$ pens and one pencil is Rs. $35$ (Given)

$\therefore$ $2x+y=35$ $⟶{eq}^n\left(i\right)$

cost of $3$ pens and $4$ pencils is Rs. $65$

$\therefore$ $3x+4y=65$ $⟶{eq}^n\left(ii\right)$

Multiplying ${eq}^n\left(i\right)$ by $4$, we get

$8x+4y=140$ $⟶{eq}^n\left(iii\right)$

Subtracting ${eq}^n\left(ii\right)$ from $\left(iii\right)$, we have

$8x+4y-3x-4y=140-65$

$\Rightarrow$ $5x=75$

$\Rightarrow$ $x=15$

Hence, the cost of $1$ pen is Rs. $15$.