Solution (By Examveda Team)

Let the investment of A in 2006 be Rs. $$x$$
Then,
$$\eqalign{ & \text{Profit = 55% of Rs. }x \cr & =\text{Rs.}\left(x\times\frac{55}{100}\right) \cr & =\text{Rs.}\left(\frac{11x}{20}\right) \cr & \therefore \frac{11x}{20} = 10.12\text{ lakh} \cr & \Rightarrow \frac{11x}{20} = 10.12\times100000 \cr & \Rightarrow \frac{11x}{20} = 1012000 \cr & \Rightarrow x = 1012000\times\frac{20}{11} \cr & \Rightarrow x = 1840000 \cr & \Rightarrow x = \text{18.4 lakh} \cr} $$
  $$\Rightarrow$$ Investment of A in 2006 = 18.4 lakh