If the expenditures of Companies A and B in 2001 were equal and the total income of the two companies was Rs. 116 lakhs, what was the total expenditure of the two companies in that year ?

In 2001,

Let income of company A = Rs. $$x$$ lakhs

=> Income of company B = Rs. $$(116 - x)$$ lakhs

Let expenditure of each company = Rs. $$y$$ lakhs

Profit % for company A

=> $$\frac{x - y}{y} \times 100 = 40$$

=> $$100x - 100y = 40y$$

=> $$100x = 40y + 100y = 140y$$

=> $$x = \frac{140y}{100} = \frac{7y}{5}$$

Profit % for company B

=> $$\frac{(116 - x) - y}{y} \times 100 = 50$$

=> $$y = 2 (116 - x) - 2y$$

=> $$3y = 232 - 2x$$

=> $$3y = 232 - (2 \times \frac{7y}{5})$$

=> $$3y = 232 - \frac{14y}{5}$$

=> $$3y + \frac{14y}{5} = 232$$

=> $$\frac{29y}{5} = 232$$

=> $$y = \frac{232 \times 5}{29} = 40$$ lakhs

$$\therefore$$ Total expenditure = $$40 + 40 = 80$$ lakhs