Solution (By Examveda Team)

Let the income of company A in 2013 = $$x$$
Let the income of company B in 2013 = (5.7 - $$x$$)
Expenditure of company A = Expenditure of company B
$$\eqalign{ & =E\, \frac{40}{100}-\frac{x-E}{E}\times100 \cr & \frac{x}{E} = 1.4\,\, . . . . . \,\left(\text{i}\right) \text{ and} \cr & \frac{45}{100} = \frac{\left(5.7-x\right)-E}{E} \cr & \Rightarrow \frac{5.7-x}{E} = 14.5\,\, . . . . .\, \left(\text{ii}\right) \cr & \text{Divide equation (ii) by (i) we get} \cr & \Rightarrow \frac{5.7-x}{E}\times\frac{E}{x}=\frac{145}{140} \cr & \Rightarrow \frac{5.7x}{x}=\frac{145}{140} \cr & \Rightarrow 5.7\times140-140x=145x \cr & \Rightarrow 798 = 285x \cr & \Rightarrow x = 2.8 \text{ lakhs} \cr & \because \frac{x}{E} = 1.4 \cr & E = 2 \text{ lakhs} \cr & \text{Total expenditure of two companies} \cr & =2+2 \cr & = 4 \text{ lakhs} \cr} $$