Solution (By Examveda Team)

$$\eqalign{ & \text{In 2010, 50} = \frac{2-E_1}{E_1}\times100 \cr & \Rightarrow 50\,E_1= 200-100\,E_1 \cr & \Rightarrow 150\,E_1 = 200 \cr & \Rightarrow E_1 = \frac{4}{3} \cr & \text{In 2011, 45} = \frac{3-E_2}{E_2}\times100 \cr & \Rightarrow 45\,E_2 = 300 - 100\,E_2 \cr & \Rightarrow 145\,E_2=300 \cr & \Rightarrow E_2= \frac{300}{145} \cr & \text{Then, }\frac{E_1}{E_2} = \frac{4}{3}\times\frac{145}{300} \cr & \Rightarrow \frac{E_1}{E_2} = \frac{29}{45} \cr & \Rightarrow E_1:E_2=29:45 \cr} $$