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

Solution(By Examveda Team)

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 $${\left( {1 + \frac{{\text{R}}}{{100}}} \right)^t}$$
$$\eqalign{ & \Rightarrow 48400 = 40000{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} \cr & \Rightarrow \frac{{484}}{{400}} = {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^2} \cr & \Rightarrow 1 + \frac{{\text{R}}}{{100}} = \frac{{22}}{{20}} \cr & \Rightarrow \frac{{\text{R}}}{{100}} = \frac{1}{{10}} \cr & \Rightarrow {\text{R}} = 10\% \cr} $$
⇔ Rate of increment = 10%