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?

Answer: Option A

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