The initial population of a country is 1,87,500. If the birth and the death rates are 13% and 9%, respectively, then find the population of the country after 2 years.

Correct option is B

Given:

Present population of city = 1,87,500

Birth rate and death rate are = 13% and 9%

Solution:

Equivalent rate of increase/decrease = 13 - 9 = 4%

So there will be net increase of 4% every year

Population next year = 1,87,500 + 4% of 1,87,500 = 1,87,500 + 7500 = 1,95,000

Population after next year = 195000 + 4% of 195000 = 195000 +7800 = 2,02,800

Alternative method 1:

Population will be =$$1,87,500\left(\frac{100+4}{100}\right)\left(\frac{100+4}{100}\right) = 2,02,800$$​

Alternative method 2:

Successive Percent = $$x + y - \frac{(x)(y)}{100}$$​​

Successive Percent = $$+4+4 + \frac{(4)(4)}{100}$$​​

= $$4+ 0.16 =4.16$$​​

(+) sign indicates there’s an increase

Hence population will be $$1,87,500(\frac{100+8.16}{100}) = 2,02,800$$​​