Three years ago, the population of a city was 50000. If the annual increase during three successive years be 5%, 8% and 10% respectively, find the present population of the city.

Given,

P = 50000

r₁ = 5%

r₂ = 8%

r₃ = 10%

By formula,

Population = $P \times \Big(1 + \dfrac{r$1}{100}\Big) \times \Big(1 + \dfrac{r2}{100}\Big) \times \Big(1 + \dfrac{r_3}{100}\Big)

Substituting the values in formula,

$\text{Present population} = 50000 \times \Big(1 + \dfrac{5}{100}\Big) \times \Big(1 + \dfrac{8}{100}\Big) \times \Big(1 + \dfrac{10}{100}\Big) \\[1em] = 50000 \times \Big(\dfrac{100 + 5}{100}\Big) \times \Big(\dfrac{100 + 8}{100}\Big) \times \Big(\dfrac{100 + 10}{100}\Big) \\[1em] = 50000 \times \Big(\dfrac{105}{100}\Big) \times \Big(\dfrac{108}{100}\Big) \times \Big(\dfrac{110}{100}\Big) \\[1em] = 50000 \times \Big(\dfrac{21}{20}\Big) \times \Big(\dfrac{27}{25}\Big) \times \Big(\dfrac{11}{10}\Big) \\[1em] = \dfrac{50000 \times 21 \times 27 \times 11}{5000} \\[1em] = 10 \times 21 \times 27 \times 11 \\[1em] = 62370.$

Hence, present population of the city = 62370.