Finding the Ratio of Persons Participating in a Survey

The question asks us to find the ratio of the number of persons participating in a survey from state S3 to the number of persons participating in a survey from state S4. We are given a table that shows the number of participants from 6 different states.

Identifying the Number of Participants for S3 and S4

From the given table, we can find the number of persons participating from state S3 and state S4:

• Number of persons from state S3 = 400
• Number of persons from state S4 = 500

Calculating the Ratio

The ratio of the number of persons from state S3 to the number of persons from state S4 is written as:

Ratio = (Number of persons from S3) : (Number of persons from S4)

Substituting the values from the table:

Ratio = 400 : 500

Simplifying the Ratio

To simplify the ratio 400 : 500, we need to find the greatest common divisor (GCD) of 400 and 500. Both numbers are divisible by 100.

• Divide the first number (400) by 100: \(400 \div 100 = 4\)
• Divide the second number (500) by 100: \(500 \div 100 = 5\)

So, the simplified ratio is 4 : 5.

In mathematical notation, this is written as \(4 \ratio 5\).

Comparing with Options

We compare our calculated ratio \(4 \ratio 5\) with the given options:

• Option 1: \(3 \ratio 5\) (Does not match)
• Option 2: \(5 \ratio 4\) (Does not match, this is the inverse ratio S4:S3)
• Option 3: \(4 \ratio 3\) (Does not match)
• Option 4: \(4 \ratio 5\) (Matches)

Therefore, the ratio of the number of persons participating in a survey from state S3 to the number of persons participating from state S4 is \(4 \ratio 5\).

Revision Table: Survey Ratio Calculation

Additional Information: Understanding Ratios

A ratio is a way to compare two or more quantities of the same kind. It shows how many times one quantity is contained in another. Ratios are often written using a colon (:) between the quantities.

• For example, the ratio of apples to oranges in a basket might be 2:3, meaning for every 2 apples, there are 3 oranges.
• Ratios can often be simplified by dividing all parts of the ratio by their greatest common divisor (GCD). This does not change the relationship between the quantities, just the numbers used to express it.
• The order of the quantities in a ratio matters. The ratio S3 : S4 is different from the ratio S4 : S3.