In a factory, the production of scooters was 40000 per year, which rose to 57600 in 2 years. Find the rate of growth per annum.

Given,

Initial Production = 40000

Production after 2 years = 57600

n = 2 years

Let the rate of growth per annum be r.

By formula,

Production after n years = $P \times \Big(1 + \dfrac{r}{100}\Big)^n$

Substituting the values in formula,

$\Rightarrow 57600 = 40000 \times \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{57600}{40000} = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{576}{400} = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \Big(\dfrac{24}{20}\Big)^2 = \Big(1 + \dfrac{r}{100}\Big)^2 \\[1em] \Rightarrow \dfrac{24}{20} = 1 + \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{24}{20} - 1 = \dfrac{r}{100} \\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{24 - 20}{20} \\[1em] \Rightarrow \dfrac{r}{100} = \dfrac{4}{20} \\[1em] \Rightarrow r = \dfrac{4 \times 100}{20} \\[1em] \Rightarrow r = 20\%$

Hence, the rate of growth per annum = 20%.