The following table shows the number of votes polled along with the percentage (%) of valid votes and ratio of valid votes of male and females among them during an election in a college for the last five years from 2018-2022. Some values are missing in the table (indicated by '-') that you are expected to calculate if required. Based on the data in the table, answer the questions that follows. Year-wise Details of Voters Polled in an Election Year Number of votes polled Percentage of valid votes polled (%) Ratio of valid votes of male and females 2018 - - 5 ∶ 3 2019 1000 - 5∶ 4 2020 2000 38% - 2021 - 60% 7 ∶ 5 2022 5000 40% -
In the year 2020, if the number of valid votes of females was 300 then what was the ratio of valid votes of males and females in the same year?
23 ∶ 15
The question asks us to determine the ratio of valid votes of males and females for the year 2020, given specific information for that year.
Let's first look at the data provided in the table for the year 2020:
| Year | Number of votes polled | Percentage of valid votes polled (%) | Ratio of valid votes of male and females |
|---|---|---|---|
| 2018 | - | - | 5 ∶ 3 |
| 2019 | 1000 | - | 5∶ 4 |
| 2020 | 2000 | 38% | - |
| 2021 | - | 60% | 7 ∶ 5 |
| 2022 | 5000 | 40% | - |
For the year 2020, we are given the following:
- Number of votes polled: 2000
- Percentage of valid votes polled: 38%
We are also given extra information for 2020 in the question:
- Number of valid votes of females: 300
We need to find the ratio of valid votes of males and females in 2020.
Calculating Total Valid Votes in 2020
First, let's calculate the total number of valid votes polled in the year 2020. The total number of votes polled was 2000, and 38% of these were valid votes.
Total valid votes = (Percentage of valid votes / 100) × Number of votes polled
Using the values for 2020:
Total valid votes in 2020 = $\frac{38}{100} \times 2000$
Total valid votes in 2020 = $38 \times 20$
Total valid votes in 2020 = $760$
So, there were 760 valid votes polled in 2020.
Determining Valid Votes for Males in 2020
We know the total valid votes in 2020 (760) and the number of valid votes for females in 2020 (300).
The total valid votes are the sum of valid votes from males and valid votes from females.
Total valid votes = Valid votes of males + Valid votes of females
We can find the valid votes of males by subtracting the valid votes of females from the total valid votes.
Valid votes of males in 2020 = Total valid votes in 2020 - Valid votes of females in 2020
Valid votes of males in 2020 = $760 - 300$
Valid votes of males in 2020 = $460$
So, there were 460 valid votes polled by males in 2020.
Calculating the Ratio of Valid Votes (Male to Female) in 2020
We have calculated the number of valid votes for males (460) and are given the number of valid votes for females (300) for the year 2020.
The ratio of valid votes of males and females is given by:
Ratio = Valid votes of males : Valid votes of females
Ratio = $460 : 300$
To simplify the ratio, we can divide both numbers by their greatest common divisor. Both 460 and 300 are divisible by 10.
Ratio = $\frac{460}{10} : \frac{300}{10}$
Ratio = $46 : 30$
Now, both 46 and 30 are divisible by 2.
Ratio = $\frac{46}{2} : \frac{30}{2}$
Ratio = $23 : 15$
The simplified ratio of valid votes of males and females in 2020 is 23 ∶ 15.
Summary of Valid Vote Calculation Steps
- Find the total number of votes polled from the table for the specified year (2020).
- Find the percentage of valid votes from the table for the same year (2020).
- Calculate the total number of valid votes using the votes polled and the valid percentage.
- Use the given number of valid votes for one category (females in this case).
- Calculate the number of valid votes for the other category (males) by subtracting the known category's valid votes from the total valid votes.
- Form the ratio of valid votes for males to females using the calculated numbers.
- Simplify the ratio to its lowest terms.
Revision Table: Key Concepts
| Concept | Description | How it Applied Here |
|---|---|---|
| Percentage Calculation | Finding a part of a whole based on a percentage. Formula: $(\text{Percentage} / 100) \times \text{Whole}$ | Used to find total valid votes from total votes polled. |
| Total vs. Parts | The total is the sum of its parts. Total Valid Votes = Valid Male Votes + Valid Female Votes. | Used to find valid male votes when total valid votes and valid female votes were known. |
| Ratio | A comparison of two quantities by division. Represented as a:b or a/b. | Used to express the relationship between the number of valid male votes and valid female votes. |
| Ratio Simplification | Dividing both parts of a ratio by their greatest common divisor to get the simplest form. | Used to simplify the ratio 460:300 to 23:15. |
Additional Information on Vote Analysis
Analyzing vote data often involves calculating percentages, ratios, and comparing numbers across different categories or years. Understanding how to convert between total votes, valid votes, and percentages is crucial. Ratios help us understand the proportion between different groups, like male and female voters, within the valid vote count. Missing data points in tables, like the ones indicated by '-', require careful calculation using the available information from other columns or external data provided in the question.
For instance, in 2018, if we knew the total valid votes, we could use the 5:3 ratio to find the number of valid male and female votes. If valid male votes were '5x' and valid female votes were '3x', the total valid votes would be '8x'. If we found '8x', we could then find '5x' and '3x'. Similarly, if we knew the percentage of valid votes in 2019, we could find the total valid votes from the 1000 votes polled and then use the 5:4 ratio to distribute them among males and females.
Data interpretation questions like this test your ability to extract relevant information from tables, perform calculations accurately, and present the results in the required format, such as a simplified ratio.
Important Questions from Tabulation
The table shows District-wise data of a number of primary school teachers posted in schools of a city.
Study the table and answer the question:
District
Male teachers
Female teachers
East
1650
2375
North
1075
2651
West
1280
1520
South
1170
1085
Central
690
859
What is the difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South?Table shows income (in Rs. ) received by 4 employees of a company during the month of December 2020 and all their income sources.
Source
Amit
Suresh
Nitin
Varun
Salary
35000
38500
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
What is the ratio of salary of Varun to his income other than salary?Study the table and answer the question:
Income (Rs.)
No. of persons
Less than 200
12
Less than 250
26
Less than 300
34
Less than 350
40
Less than 400
50
What is the percentage of persons earning Rs. 250 or more?The following table shows the annual profit of a company (in Rs. lakh).
2014-2015
2015-2016
2016-0217
2017-2018
2018-2019
625
690
725
775
815
The period which has the maximum percentage increase in profit over the previous year is:
The table given below shows the number of persons participating in a survey from 6 different states.
States Persons S1 100 S2 200 S3 400 S4 500 S5 600 S6 800 What is the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4?
