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.
If the ratio of taxpayers to other persons in the same age group below 30 years is 1 : 2, then what is the number of taxpayers (in lakhs) in that age group?
0.7
Understanding the Population Data and Taxpayers Calculation
The problem provides us with age-wise population percentages for a city and the total number of persons below 40 years. We are also given a ratio of taxpayers to other persons in the age group below 30 years. Our goal is to find the number of taxpayers in the age group below 30 years.
Analyzing the Provided Data Table
Let's look at the age-wise population percentages:
| Age group | Percentage |
|---|---|
| Below 30 years | 14.00 |
| 30–34.99 | 29.75 |
| 35–39.99 | 26.25 |
| 40–44.99 | 04.00 |
| 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. The age groups below 40 years are:
- Below 30 years (14.00%)
- 30–34.99 (29.75%)
- 35–39.99 (26.25%)
Calculating the Total Percentage Below 40 Years
First, let's find the total percentage of the population that is below 40 years of age. This is the sum of the percentages for the three age groups mentioned above:
Percentage below 40 years \(= \text{Percentage(Below 30)} + \text{Percentage(30–34.99)} + \text{Percentage(35–39.99)}\)
Percentage below 40 years \(= 14.00\% + 29.75\% + 26.25\%\)
Percentage below 40 years \(= 70.00\%\)
Determining the Total Population of the City
We know that 70% of the total population is equal to 10.5 lakhs. Let the total population of the city be \(P\).
\(70\% \text{ of } P = 10.5 \text{ lakhs}\)
\(0.70 \times P = 10.5\)
\(P = \frac{10.5}{0.70}\)
\(P = \frac{10.5 \times 10}{0.70 \times 10} = \frac{105}{7}\)
\(P = 15 \text{ lakhs}\)
So, the total population of the city is 15 lakhs.
Finding the Number of Persons Below 30 Years
The table shows that the percentage of the population below 30 years is 14.00%. We can now calculate the number of persons in this age group using the total population.
Number of persons below 30 years \(= 14.00\% \text{ of Total Population}\)
Number of persons below 30 years \(= 0.14 \times 15 \text{ lakhs}\)
Number of persons below 30 years \(= 2.1 \text{ lakhs}\)
Calculating the Number of Taxpayers in the Below 30 Years Age Group
We are given that the ratio of taxpayers to other persons in the age group below 30 years is 1 : 2. This means that for every 1 taxpayer, there are 2 persons who are not taxpayers in this group.
The total number of parts in the ratio is \(1 + 2 = 3\).
Out of these 3 parts, 1 part represents taxpayers and 2 parts represent other persons.
The fraction of taxpayers in this age group is \(\frac{1}{3}\).
Number of taxpayers below 30 years \(= \left(\text{Fraction of taxpayers}\right) \times \left(\text{Number of persons below 30 years}\right)\)
Number of taxpayers below 30 years \(= \frac{1}{3} \times 2.1 \text{ lakhs}\)
Number of taxpayers below 30 years \(= 0.7 \text{ lakhs}\)
Conclusion
Based on the data and calculations, the number of taxpayers in the age group below 30 years is 0.7 lakhs.
Revision Table: Key Calculations Summary
| Description | Calculation | Result |
|---|---|---|
| Total % below 40 years | \(14.00\% + 29.75\% + 26.25\%\) | \(70\%\) |
| Total Population (lakhs) | \(\frac{10.5 \text{ lakhs}}{70\%}\) | \(15 \text{ lakhs}\) |
| Persons below 30 years (lakhs) | \(14.00\% \times 15 \text{ lakhs}\) | \(2.1 \text{ lakhs}\) |
| Taxpayers below 30 years (lakhs) | \(\frac{1}{3} \times 2.1 \text{ lakhs}\) | \(0.7 \text{ lakhs}\) |
Additional Information: Data Interpretation Tips
Solving data interpretation problems often requires careful reading of the question and the provided data (tables, charts, graphs). Here are some tips:
- Read the question carefully: Understand exactly what is being asked. Pay attention to units (like lakhs in this case).
- Analyze the data: Look at the table or chart provided. Understand the categories, values, and what they represent.
- Identify relevant data: Not all data provided may be needed to answer a specific question. Focus on the parts relevant to the calculation.
- Break down the problem: If the problem involves multiple steps, break it down into smaller, manageable calculations.
- Check percentages and ratios: Understand how to work with percentages to find absolute values and how to use ratios to divide a quantity.
- Be mindful of units: Ensure consistency in units throughout your calculations.
In this specific problem, understanding how to use the percentage for a combined age group (below 40) to find the total population was a crucial first step before focusing on the specific age group (below 30) and the taxpayer ratio.
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
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Number of
Students
1 – 10
5
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8
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10
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13
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18
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17
61 – 70
12
71 – 80
7
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