If the incomes of Company B in 2002 and 2003 were in the ratio of 3:4 respectively, what was the respective ratio of expenditures of that company in these two years ?

Let income of company B in 2002 = Rs. $$3x$$ lakhs

=> income of company B in 2003 = Rs. $$4x$$ lakhs

Let expenditures of company B in 2002 and 2003 respectively = $$E_1$$ and $$E_2$$

Profit % in 2002

=> $$\frac{3x - E_1}{E_1} \times 100 = 45$$

=> $$300x - 100 E_1 = 45 E_1$$

=> $$300x = 45 E_1 + 100 E_1 = 145 E_1$$

=> $$E_1 = \frac{300x}{145} = \frac{60x}{29}$$

Profit % in 2003

=> $$\frac{4x - E_2}{E_2} \times 100 = 55$$

=> $$400x - 100 E_2 = 55 E_2$$

=> $$400x = 55 E_2 + 100 E_2 = 155 E_2$$

=> $$E_2 = \frac{400x}{155} = \frac{80x}{31}$$

$$\therefore$$ $$\frac{E_1}{E_2} = \frac{\frac{60x}{29}}{\frac{80x}{31}}$$

= $$\frac{60}{29} \times \frac{31}{80} = 93 : 116$$