Question

In a factory, the production of scooters rose to $48400$ from $40000$ in $2$ years. Find the rate of growth per annum.

Answer 1

Let the rate of growth per annum be $R$.

We have, Present production $=48400$ scooters.

Previous production $=40000$ scooters

Number of years $=2$

$\therefore 48400=40000\times {(1+\frac{R}{100})}^2$

$\Rightarrow \frac{48400}{40000}={(1+\frac{R}{100})}^2$

$\Rightarrow \frac{484}{400}={(1+\frac{R}{100})}^2$

$\Rightarrow \frac{121}{100}={(1+\frac{R}{100})}^2$

$\Rightarrow {(1+\frac{R}{100})}^2={\left(\frac{11}{10}\right)}^2$

$\Rightarrow 1+\frac{R}{100}=\frac{11}{10}$

$\Rightarrow \frac{R}{100}=\frac{11}{10}-1$

$\Rightarrow \frac{R}{100}=\frac{1}{10}$

$\Rightarrow R=\frac{100}{10}=10$

Hence, the required rate of growth $=10\%$ per annum.