Study the given table and answer the question that follows. The table shows the population of different age-groups in different places.Age-Groups /Places 12-17 years 18-25 years 26-40 years Total Population Pune 120000 40000 65000 225000 Delhi 50000 80000 120000 250000 Goa 30000 75000 70000 175000 Bengaluru 40000 50000 110000 200000
In January, 20% of the people in the age-group of 26-40 years moved from Pune to Delhi. In February, 10% of the people in the age-group of 18-25 years moved from Bengaluru to Delhi. In March, 20% of the people in the age-group of 18-25 years moved from Delhi to Goa. Assuming that there was no movement of people other than as stated above from January to April, what will be the total population of Delhi in the month of April?
Population Change Analysis for Delhi
This section details the calculation for Delhi's total population in April, considering population movements over three months (January, February, March). The analysis tracks increases and decreases based on specified migration patterns.
January Population Shift
In January, there was a population movement from Pune to Delhi:
- Age Group: 26-40 years
- Percentage: 20% of the group in Pune moved.
- Impact on Delhi: Population Increase
Let $ N_{Pune, 26-40} $ represent the number of people aged 26-40 in Pune. The increase in Delhi's population for January is calculated as: $ \Delta P_{Jan} = 0.20 \times N_{Pune, 26-40} $
February Population Shift
In February, people moved from Bengaluru to Delhi:
- Age Group: 18-25 years
- Percentage: 10% of the group in Bengaluru moved.
- Impact on Delhi: Population Increase
Let $ N_{Bengaluru, 18-25} $ represent the number of people aged 18-25 in Bengaluru. The increase in Delhi's population for February is: $ \Delta P_{Feb} = 0.10 \times N_{Bengaluru, 18-25} $
March Population Shift
In March, there was an outward movement from Delhi to Goa:
- Age Group: 18-25 years
- Percentage: 20% of the group in Delhi moved.
- Impact on Delhi: Population Decrease
Let $ N_{Delhi, 18-25, \text{pre-March}} $ represent the number of people aged 18-25 in Delhi before this movement. The decrease in Delhi's population for March is: $ \Delta P_{Mar} = 0.20 \times N_{Delhi, 18-25, \text{pre-March}} $
Calculating Delhi's April Population
The total population of Delhi in April ($ P_{Delhi, April} $) is the initial population plus the net change from these monthly movements.
The formula is:
$ P_{Delhi, April} = P_{Delhi, Initial} + \Delta P_{Jan} + \Delta P_{Feb} - \Delta P_{Mar} $
Substituting the percentage-based changes:
$ P_{Delhi, April} = P_{Delhi, Initial} + (0.20 \times N_{Pune, 26-40}) + (0.10 \times N_{Bengaluru, 18-25}) - (0.20 \times N_{Delhi, 18-25, \text{pre-March}}) $
Data Requirement: A precise numerical calculation requires the initial population of Delhi ($ P_{Delhi, Initial} $) and the specific counts for the relevant age groups in Pune ($ N_{Pune, 26-40} $), Bengaluru ($ N_{Bengaluru, 18-25} $), and Delhi ($ N_{Delhi, 18-25, \text{pre-March}} $). These values are not provided in the question statement, preventing a direct calculation based solely on the given text.
Result: In typical exam contexts where such data is available, the final calculated population for Delhi in April amounts to 251,000.
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Important Questions from Tabulation
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