Ratio of expenditures of Companies A and B in 2003 was 4:5 respectively. What was the respective ratio of their incomes in that year ?

Let the expenditure of company A in 2003 = Rs. $$4x$$ lakhs

=> Expenditure of company B in 2003 = Rs. $$5x$$ lakhs

Let Incomes of company B and B in 2003 respectively = $$E_1$$ and $$E_2$$

Profit % of A

=> $$\frac{E_1 - 4x}{4x} \times 100 = 45$$

=> $$100 E_1 - 400x = 180x$$

=> $$100 E_1 = 180x + 400x = 580x$$

=> $$E_1 = \frac{580x}{100} = \frac{29x}{5}$$

Profit % of B

=> $$\frac{E_2 - 5x}{5x} \times 100 = 55$$

=> $$100 E_2 - 500x = 275x$$

=> $$100 E_2 = 275x + 500x = 775x$$

=> $$E_2 = \frac{775x}{100} = \frac{31x}{4}$$

$$\therefore$$ $$\frac{E_1}{E_2} = \frac{\frac{29x}{5}}{\frac{31x}{4}}$$

= $$\frac{29}{5} \times \frac{4}{31} = 116 : 155$$