If the total amount invested by the two companies in 2009 was Rs. 27 lakh, while the amount invested by Company B was 50% of the amount invested by Company A, what was the total profit earned by the two companies together?

Let the investment of A in 2009 be Rs. $$x$$
Then,
Investment of B
$$\eqalign{ & = \text{50% of Rs. }x\cr & =\text{Rs.} \left(x\times\frac{50}{100}\right) \cr & =\text{Rs. } \frac{x}{2} \cr & \therefore \left(x+\frac{x}{2}\right) = 27 \text{ lakh} \cr & \Rightarrow \frac{3x}{2} = 27 \text{ lakh} \cr & \Rightarrow x = \left(27\times\frac{2}{3}\right) \text{lakh} \cr & \Rightarrow x = \text{18 lakh} \cr} $$
  ∴ Investment of A in 2009 = Rs. 18 lakh and investment of B = Rs. 9 lakh.

$$\eqalign{ & \text{Profit of A} \cr & =\text{Rs.} \left(18\text{ lakh}\times \frac{75}{100}\right) \cr & = \text{Rs. 13.50 lakh} \cr & \text{Profit of B} \cr & =\text{Rs.} \left(9\text{ lakh}\times \frac{80}{100}\right) \cr & = \text{Rs. 7.20 lakh} \cr & \therefore \text{Total profit of A and B} \cr & = \text{Rs.}\left(13.50+7.20\right)\text{lakh} \cr & = \text{Rs. 20.70 lakh} \cr} $$