Initial Village Population

The starting population of the village is given as 2,90,000.

Population Increase in the First Year

The population increased by 5% in the first year.

• Calculate the increase amount:

  Increase = Initial Population $\times$ Percentage Increase

  Increase = $2,90,000 \times \frac{5}{100}$

  Increase = $2,900 \times 5 = 14,500$

• Calculate the population after the first year:

  Population (Year 1) = Initial Population + Increase

  Population (Year 1) = $2,90,000 + 14,500 = 3,04,500$

Population Increase in the Second Year

The population further increased by 30% in the second year, based on the population at the end of the first year.

• Calculate the increase amount for the second year:

  Increase = Population (Year 1) $\times$ Percentage Increase

  Increase = $3,04,500 \times \frac{30}{100}$

  Increase = $3,045 \times 30 = 91,350$

• Calculate the final population after the second year:

  Population (Year 2) = Population (Year 1) + Increase

  Population (Year 2) = $3,04,500 + 91,350 = 3,95,850$

Final Population Calculation

The population of the village after two years is 3,95,850.