Question

Find the ratio of (a) Rs.5 to 5 paise (b) 30 days to 36 hours.

Answer 1

Hint: We cannot directly take the ratios between the quantities simply as it is. For the same we have to first convert the given quantities into the same unit. Use 1 rupee = 100 paise. Use 1day = 24hours. After the conversions into a single unit, take the ratio of corresponding terms and report the answer.

Complete step by step answer:
We are given two questions both of which are to find ratios between quantities. Let us first consider sub-question (a). Here we are asked to find the ratio between Rs.5 and 5 paise which are in two different units of money, namely rupees and paisa respectively.
Before we take the ratio we are to convert one of the given quantities into the unit of the other. We know the fact that one rupee equals a hundred paise (Re.1=100 paise). So, here we can either convert Rs.5 into paise or we can convert 5 paise into rupees.
Here, we convert Rs.5 into paises.
\[\begin{align}
  & \operatorname{Re}.1=100\text{ }paise \\
 & \therefore Rs.5=5\times 100\,paise=500\,paise \\
\end{align}\]
$\therefore $ Ratio between Rs.5 and 5 paise = $\dfrac{Rs.5}{5\,paise}=\dfrac{500\,paise}{5\,paise}=\,\dfrac{100}{1}$
Hence, the ratio of Rs.5 to 5 paise is 100 : 1.
Now let us consider sub-question (b). Here we are asked to find the ratio between 30 days and 36 hours which are in two different units of time, namely days and hours (respectively).
Before we take the ratio we are to convert one of the given quantities into the unit of the other. We know the fact that one day equals twenty four hours (1 day=24 hours). So, here we can either convert 30 days into hours or we can convert 36 hours into days.
Here, we convert 30 days into hours.
$1\,day=24\,hours$
$\therefore 30\,days=30\times 24\,hours=720\,hours$
$\therefore $ Ratio between 30 days and 36 hours =$\dfrac{30\,days}{36\,hours}=\dfrac{720\,hours}{36\,hours}=\dfrac{20}{1}$
Hence, the ratio of 30 days to 36 hours is 20 : 1.

Note:
The conversions are very important in these type of questions. One must always do the necessary conversions in order to get the correct ratio.
Alternate method :
In sub-question (a) we could have converted 5 paise into rupees and in sub-question (b) we could have converted 36 hours into days and taken the ratios. The answer would remain the same.