Question

Express the given ratio in its simplest form: - 10 paisa: 1 rupee.

Answer 1

Hint: Assume the given ratio as R. Consider 10 paisa as the numerator and 1 rupee as the denominator of the fraction. Convert the unit rupee into paise by using the relation 1 rupee = 100 paise. Cancel the unit paisa from the numerator and the denominator. Cancel the common factors to simplify the fraction and get the simplest form of the ratio.

Complete step by step answer:
Here we have been asked to find the simplest form of the ratio 10 paisa: 1 rupee. That means we have to cancel the common factors present in the numbers given. Let us assume the given ration as R, so we have,
$\Rightarrow $ R = 10 paisa: 1 rupee
To cancel the unit we have to make the units of the currency same, so using the relation 1 rupee = 100 paise we get,
$\Rightarrow $ R = 10 paisa: 100 paisa
Converting the ratio into the fraction we must have 10 paisa as the numerator and 100 paisa as the denominator of the fraction, so we get,
$\Rightarrow R=\dfrac{10\text{ paisa}}{100\text{ paisa}}$
Cancelling the unit of currency and common factors to simplify the above fraction we get,
\[\begin{align}
  & \Rightarrow R=\dfrac{10}{10\times 10} \\
 & \Rightarrow R=\dfrac{1}{10} \\
\end{align}\]
Converting the simplified form of the fraction back into the ratio we get,
$\therefore $ R = $1:10$
Hence, the simplest form of the given ratio is $1:10$.

Note: Note that the ratio is a pure number that means it has no units. When we multiply a fraction with 100 then it becomes a percentage. In the above solution we have converted the unit rupee into paise, however you can also convert paisa into rupee by dividing 10 paisa with 100. You have converted only one unit such that the two units get cancelled.