Direction : Consider the following data for the two (02) items that follow : The table below gives the age-wise population percentage of a city : Age group Percentage Below 30 years 14.00 30–34.99 29.75 35–39.99 26.25 40–44.99 0 45–49.99 18.50 50 years and above 11.50 The number of persons below the age of 40 years is 10.5 lakhs.
What is the total population of the city (in lakhs)?
15
Understanding the City Population Data
The problem provides data about the age distribution of a city's population in percentages. It also gives us a crucial piece of information: the actual number of people below 40 years of age. Our goal is to use this information to calculate the total population of the city.
First, let's look at the provided population data based on age groups:
| Age group | Percentage |
|---|---|
| Below 30 years | 14.00 |
| 30–34.99 | 29.75 |
| 35–39.99 | 26.25 |
| 40–44.99 | 0 |
| 45–49.99 | 18.50 |
| 50 years and above | 11.50 |
We are told that the number of persons below the age of 40 years is 10.5 lakhs.
Calculating the Percentage of Population Below 40 Years
To find the total percentage of the population below 40 years, we need to sum the percentages of all age groups that fall under this category. From the table, the age groups below 40 years are:
- Below 30 years
- 30–34.99 years
- 35–39.99 years
The age group 40–44.99 and older groups are not below 40 years. Now, let's add their percentages:
Percentage of population below 40 years \( = \) Percentage (Below 30) \( + \) Percentage (30–34.99) \( + \) Percentage (35–39.99)
Percentage below 40 years \( = 14.00\% + 29.75\% + 26.25\%\)
Percentage below 40 years \( = 70.00\%\)
So, 70% of the city's total population is below 40 years of age.
Finding the Total City Population
We know that 70% of the total population corresponds to 10.5 lakhs people. Let the total population of the city be \(T\) lakhs.
We can set up the equation:
\(70\% \text{ of } T = 10.5 \text{ lakhs}\)To solve for \(T\), we convert the percentage to a decimal:
\(0.70 \times T = 10.5\)Now, divide both sides by 0.70 to find \(T\):
\(T = \frac{10.5}{0.70}\) \(T = \frac{10.5 \times 10}{0.70 \times 10} = \frac{105}{7}\) \(T = 15\)The total population of the city is 15 lakhs.
Conclusion
By calculating the total percentage of the population below 40 years from the given age group percentages and using the provided number of people in that category, we were able to determine the total population of the city.
The total population of the city is 15 lakhs.
Revision Table: Key Data Points
| Description | Value |
|---|---|
| Population below 40 years (Number) | 10.5 lakhs |
| Population percentage below 40 years | 70% |
| Relationship | 70% of Total Population = 10.5 lakhs |
| Calculated Total Population | 15 lakhs |
Additional Information: Working with Percentages in Population Data
When dealing with population data presented as percentages, it's important to remember that percentages represent parts of a whole. The sum of percentages for all categories should ideally be 100% (although sometimes slight rounding differences might occur in real data). If you know the percentage that corresponds to a specific count (like the number of people below 40), you can find the total count (total population) using the formula:
Total = \(\frac{\text{Part (as a number)}}{\text{Percentage (as a decimal)}}\)
In this problem:
- Part (number of people below 40) = 10.5 lakhs
- Percentage (below 40) = 70% = 0.70 (as a decimal)
- Total Population = \(\frac{10.5}{0.70} = 15\) lakhs
This method is useful for scaling up from a known part to the entire population.
Similar Questions
Consider the following data with regard to production of cars (In lakhs):
Year 2015
Year 2016
Country A
35
38
Country B
45
47
Country C
88
93
Country D
75
79
Country E
58
60.9
In which of the countries, the production of cars has increased by more than or equal to 5% in 2016 over 2015?The following table shows the marks of 90 students in a test of 80 marks:
Marks
Number of
Students
1 – 10
5
11 – 20
8
21 – 30
10
31 – 40
13
41 – 50
18
51 – 60
17
61 – 70
12
71 – 80
7
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