Question

In a factory, the production of scooters rose to 46305 from 40000 in 3 years. Find the annual rate of growth of the production of scooters.

Answer 1

Production of scooters 3 years ago (P) = 40000
Present production (A) = 46305
Period (n) = 3 years
$\because A=P{(1+\frac{R}{100})}^n$
$46305=40000{(1+\frac{R}{100})}^3$
$\Rightarrow {(1+\frac{R}{100})}^3=\frac{46305}{40000}=\frac{9261}{8000}={\left(\frac{21}{20}\right)}^3$
Comparing, we get:
$1+\frac{R}{100}=\frac{21}{20}=1+\frac{1}{20}$
$\therefore \frac{R}{100}=\frac{1}{20}\Rightarrow R=\frac{100}{20}=5$
$\therefore$ Rate of growth in production $=5\%$ p.a