Question

Given that the total cost of $5$ erasers, $7$ sharpeners and $9$ pencils in Rs.$100$ and the total cost of $2$ erasers, $6$ sharpeners and $10$ pencils is Rs.$80$. What is the total cost (in Rs.) of one eraser one sharpener and one pencil?

• A. $10$
• B. $15$
• C. $20$
• D. Data not sufficient

Answer 1

Answer: (C)

$20$

Suppose one eraser, one sharpener and one pencil cost $e,s$ and $p$ rupees respectively.

Given:

$5e+7s+9p=100$ ........... $\left(1\right)$ and $2e+6s+10p=80$ ........... $\left(2\right)$

So, from $\left(2\right)$

$e+3s+5p=40$ $⟹$ $e=40-3s-5p$

Substituting in $\left(1\right)$ we get,

$5(40-3s-5p)+7s+5p=40$ by solving we get $s=10-2p$ ......... $\left(3\right)$

Substitute in $\left(2\right)$ we get,

$e-p=10$ ........... $\left(4\right)$

Adding $\left(3\right)$ and $\left(4\right)$ we get,

$e+s+p=20$.

Hence, option C is correct.