Q21. The population of a village is 1,00,000. Every year, villagers move to cities in search of jobs and the
population of the village decreases at a rate of 5% per annum. How many villagers will migrate in 2
years?
1. 9,750
2. 9,950
3. 9,500
4. 10,000

Introduction to Population Decline in a Village

Population decline is a common demographic challenge faced by rural areas. Many villagers migrate to cities in search of better job opportunities, leading to a gradual reduction in the village population. Understanding the rate of population decline and calculating the total migration over time is essential for demographic analysis and planning.

Problem Statement

The population of a village is initially 1,00,000. Every year, the population decreases at a rate of 5% per annum due to migration. The objective is to calculate how many villagers will have migrated in 2 years.

Formula for Population Decline

The population after n years with an annual percentage decrease can be calculated using the formula:

Step 1:

Initial population = 1,00,000
Rate of decrease = 5% per annum
Number of years = 2

Step 2: Population After 2 Years

Using the formula:

Step 3: Number of Migrants

The number of villagers who migrated in 2 years:

Migrants=1,00,000−90,250

$$=\; 9,750$$

Final Answer

Therefore, the number of villagers who migrated from the village over 2 years is 9,750.

Understanding Population Decline and Its Impact

• Rural-to-urban migration is driven by factors such as lack of employment opportunities, better infrastructure in cities, and improved educational and healthcare facilities.
• A steady population decline in villages can lead to labor shortages, reduced agricultural output, and weakened local economies.

Conclusion

The population of the village decreased from 1,00,000 to 90,250 over two years due to a migration rate of 5% per annum. As a result, 9,750 villagers moved to cities in search of better job opportunities. Understanding population decline is essential for planning and improving rural development strategies.

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