If the expenditure of company A and B in 2013 were equal and the total incomes of the two companies was Rs. 5.7 lakhs. what was the total expenditure of the two companies in 2013?

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