Question

The cost of a pen is Rs $10$ and the cost of a pencil is Rs $2$. How many times is the cost of a pen that of a pencil?

Answer 1

Hint: We will calculate the ratio of the cost of the pen to the ratio of the cost of the pencil to get the required answer. Before doing this we need to be sure that both the quantities have the same unit as here we have the unit Rs. if we are given a different unit, then we need to convert it into the same unit because the number of quantities of any item is uniless.

Complete step-by-step solution
Given that,
The cost of a pen is Rs $10$ and the cost of a pencil is Rs $2$.
Now the ratio of the cost of the pen to the cost of pencil is given by
$\begin{align}
  & \dfrac{\text{pen}}{\text{pencil}}=\dfrac{10}{2} \\
 & \Rightarrow \dfrac{\text{pen}}{\text{pencil}}=5 \\
 & \Rightarrow \text{pen}=5\left( \text{pencil} \right) \\
\end{align}$
So, the cost of the pen is equal to Five times the cost of the pencil.

Note: While taking ratios we need to keep an eye on the units of the given variables. In this problem we the given two costs (cost of pen and cost of the pencil) are in rupees, so we can directly find the ratio of the variables. If anyone of the costs of a pen or the cost of the pencil is given in paise, we need to convert the units of one variable into another variable after that only we can find the ratio of the two variables. We have the relation between rupee and paise as $1$ rupee $=$$100$ paise, from this relation we can convert one cost of a variable into another cost of a variable.