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.
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Important Questions from Tabulation
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
38000
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
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Country Years A B Y1 175 285 Y2 200 300 Y3 150 125 Y4 75 85 Y5 50 95 K1 = The value of average GDP of country A in all the 5 years.
K2 = The value of average GDP of country B in all the 5 years.
What is the value of (K1 + K2)?
Study the Table Properly and answer by interpreting the data
The table shows the percentage population of five districts in a state below poverty line and the proportion of males and females.
District Percentage of population
below poverty levelProportion of Male and Female Below poverty line (M:F) Above poverty Line (M:F) D1 15 2 : 3 3 : 2 D2 18 3 : 4 7 : 5 D3 20 2 : 5 3 : 4 D4 25 5 : 2 4 : 3 D5 12 3 : 7 2 : 7 If the total population in the district D3 is 40,000, then what is the population of below poverty line in the district D3, ?
The table given below shows the marks obtained by 4 students in 5 subjects. The maximum marks of each subject is 100.
Subjects
Students
P1
P2
P3
P4
S1
89
100
92
91
S2
62
52
72
37
S3
57
55
70
65
S4
76
85
76
58
S5
85
70
66
62
What is the total percent marks of P4?
The data given below shows the number of people who have saved a certain amount of money.
Savings
(in Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the mode of the given data?
