Find the average increase rate, if increase in the population in the first year is 30%

Let 100 be the original population. 1st year’s population increased = 30% So, Population after first year = (100 + 30% of 100) = 130 Population in second year increases by 40%, Then Population = (130 + 40% of 130) = 182 The final population become 182 which was originally at 100. It means there is 82% increment in the population in 2 years So, Average increment $=\frac{82}{2}=41 \%$

Alternate Solution:

Increase in population is given by, 100 == 30% ↑⇒ 130 == 40% ↑ ⇒ 182 Hence, average increase $=\frac{82}{2}=41 \%$