In a factory, the production of cycles rose to 48400 from 40000 in 2 years. The rate of growth per annum is ?

Answer: Option D

The production of cycles rose to 48400 from 40000 in 2 years
⇒ Present production = 40000
⇒ After two years = 48000
⇒ Time = 2 years
⇒ Rate of increment = ?
According to the question,
Production after 2 years = Present production $${\left(1+\frac{\text{R}}{100}\right)}^t$$
$$\begin{array}{rl}& \Rightarrow 48400=40000{\left(1+\frac{\text{R}}{100}\right)}^2\\ & \Rightarrow \frac{484}{400}={\left(1+\frac{\text{R}}{100}\right)}^2\\ & \Rightarrow 1+\frac{\text{R}}{100}=\frac{22}{20}\\ & \Rightarrow \frac{\text{R}}{100}=\frac{1}{10}\\ & \Rightarrow \text{R}=10\%\end{array}$$
⇔ Rate of increment = 10%