Question

In a factory, the production of motor bikes was 40,000 in a particular year, which rose to 48,400 in two years. Find the growth rate per annum, if it was growing uniformly during two years.

Answer 1

Hint: The growth rate can be calculated by using the following formula. \[\]
\[\text{Rate of growth = }\dfrac{\left[ \left( \text{final production}-\text{initial production} \right) \right]}{\text{initial production}}\text{ }\!\!\times\!\!\text{ 100}\text{.}\]
Here, production of motorbikes in particular year is 40,000 and its production rose to 48,400 in two years.

Complete step-by-step answer:
Given that,
Initial production=40,000
 Final production =48,400 in two years.
Therefore, \[\text{rate of growth in two years =}\left[ \dfrac{\left( \text{final production}-\text{initial production} \right)}{\text{initial production}} \right]\text{ }\!\!\times\!\!\text{ 100}\]
\[=\left[ \dfrac{\left( 48,400-40,000 \right)}{40,000} \right]\times 100\]
\[=\left[ \dfrac{8,400}{40,000} \right]\times 100\]
\[=\dfrac{84}{4}\]
=21
Therefore, the rate of growth of production of bikes in two years is 21%.
Given that the rate of growth of production of bikes is uniform.
\[\Rightarrow \] The rate of growth of bikes per year is half of the rate of growth of bikes per two years.
\[\Rightarrow \text{the rate of growth of bikes per year = }\dfrac{\text{rate of growth of bikes per two years}}{\text{2}}\text{.}\]
\[\Rightarrow \] Rate of growth in the year is 10.5%.
Therefore, the rate of growth per annum is 10.5%.

Note: The possible mistake that could occur in this question is if you took 21% as your final answer, it should be noted that the growth rate of 21% is of two years and in the question the growth rate per annum or 1 year is asked.