If the expenditure of company E in years 2000 and 2001 was same, what was the ratio of the incomes of the company in the same year respectively?

Let the expenditure of company E in both years = Rs. $$x$$

and Income of company E in 2000 and 2001 resp = $$I_1$$ and $$I_2$$

Profit % resp for 2000 and 2001 = 45 % & 55 %

=> $$\frac{I_1 - x}{x} \times 100 = 45$$

=> $$100 I_1 - 100x = 45x$$

=> $$100 I_1 = 100x + 45x = 145x$$

=> $$I_1 = \frac{145x}{100}$$

For the year 2001,

=> $$\frac{I_2 - x}{x} \times 100 = 55$$

=> $$100 I_2 - 100x = 55x$$

=> $$100 I_2 = 100x + 55x = 155x$$

=> $$I_2 = \frac{155x}{100}$$

$$\therefore \frac{I_1}{I_2} = \frac{\frac{145x}{100}}{\frac{155x}{100}}$$

= $$\frac{145}{155} = \frac{29}{31}$$

= $$29 : 31$$