Question

A pencil costs ₹ 5 more than the cost of an eraser. The total cost of 5 pencils and 10 erasers is ₹ 100. Find the cost of a pencil and the cost of an eraser?

• A. Eraser - ₹ 15
  Pencil - ₹ 20
• B. Eraser - ₹ 10
  Pencil - ₹ 15
• C. Eraser - ₹ 5
  Pencil - ₹ 10
• D. Eraser - ₹15
  Pencil - ₹ 10

Answer 1

The correct option is C Eraser - ₹ 5

Pencil - ₹ 10
Let the cost of an eraser be ₹ $x$.
$\therefore$ Cost of pencil = ₹ (x+5).

Now, the cost of 5 pencils will be $5\times (x+5)=5(x+5)$
The cost of 10 erasers will be $10\text{times}x=10x$
Given, the total cost of 5 pencils and 10 erasers is ₹ 100
$\Rightarrow 5(x+5)+10x=100$
$\Rightarrow 5x+25+10x=100$
$\Rightarrow 15x=100-25$
$\Rightarrow 15x=75$
$\Rightarrow x=\frac{75}{15}=5$

$\therefore$The cost of an eraser is ₹ 5.
The cost of a pencil is
$=x+5=5+5=₹10$.