The production of scooters rose to $48400$ from $40000$. If the rate of growth is $10\%$, then the time required is

Let the initial production be $P_0=40000$, final production be $P_n=48400$, and growth rate be $R=10\%$.
Using the exponential growth formula:

$$P_n=P_0\times {\left(1+\frac{R}{100}\right)}^n$$

$$48400=40000\times {\left(1+\frac{10}{100}\right)}^n$$

$$\frac{48400}{40000}={\left(\frac{11}{10}\right)}^n$$

$$\frac{484}{400}={\left(\frac{11}{10}\right)}^n$$

Simplifying the fraction by dividing both parts by $4$:

$$\frac{121}{100}={\left(\frac{11}{10}\right)}^n$$

$${\left(\frac{11}{10}\right)}^2={\left(\frac{11}{10}\right)}^n$$

Equating the bases, we find:

$$n=2\text{ years}$$