Question

Find the ratio of the following:
1. \[30\]minutes to \[1.5\]hours
2. \[55\]paise to \[Rs.1\]

Answer 1

Hint: The quotient of one quantity divided by the other is a relationship between two quantities.
For instance, if a box contains six red marbles and four blue marbles, the ratio of red to blue marbles is 6:4, or 6:4.
The first term of a ratio is called antecedent and the second term is called consequent. This type of ratio has no units.
If different quantities are compared, this special type of ratio is called a rate and it has units.

Complete step by step answer:
We are given the time period: \[30\]minutes to \[1.5\]hours and amount : \[55\]paise to \[Rs.1\].
We have to find the ratio of the given as follows.
1. \[30\]minutes to \[1.5\]hours
Here, We need to convert hours into minutes,
\[1.5\]hours = \[1.5 \times 60\]minutes
We know that, (\[1\]hour = \[60\]minutes)
\[ = \dfrac{{15}}{{10}} \times 60\]
\[ = 15 \times 6\]
\[ = 90\] minutes.
Now, finding the ratio then
Ratio \[ = \dfrac{{30\min }}{{90\min }}\]
\[ = \dfrac{{30}}{{90}} \]
On simplifying the division, we can get
\[= \dfrac{3}{9}\]
\[ = \dfrac{1}{3}\]
Ratio \[ = \dfrac{1}{3}\]
Therefore, Required Ratio = \[1:3\]

2. \[55\] paise to \[Rs.1\]
Here, First, we need to convert Rs into paise
We know that,
\[Rs.1 = 1 \times 100paise\]
\[Rs.1 = 100paise\]
Now, we have to find the ratio, then
Ratio \[ = \dfrac{{55paise}}{{100paise}}\]
\[ = \dfrac{{55}}{{100}}\]
On simplifying the division, we can get
\[ = \dfrac{{11}}{{20}}\]
Therefore, Required Ratio = \[11:20\]

Hence, The ratio of the given question is,
\[30\]minutes to \[1.5\] hours - \[1:3\]
\[55\]paise to \[Rs.1\]- \[11:20\]

Note: Ratio can be used to solve both statistical and real-world problems.
To begin, we can use ratios to fill in tables.
When we compare two items, we get ratios. For the sake of convenience, they are normally simplified to the simplest words.
As an example, a school with \[1000\] students and \[50\] teachers has a \[20:1\] student/teacher ratio.
The golden ratio of classical architecture is an example of an aspect ratio, which is the width to height ratio of a rectangle.
The resulting equation is called a proportion when two ratios are set equal to each other.