Question

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

• A. 26:45
• B. 29:56
• C. 45:58
• D. 56:29
• E. None of the above

Answer 1

The correct option is C 45:58

Let the income of company B in 2002 and 2003 be Rs 3x and Rs 4x respectively.
Let respective expenditures be Rs $y_1$ and Rs $y_2$
For the year 2002.
$45=\frac{3x-y_1}{y_1}\times 100$
$\Rightarrow 3x-y_1=\frac{45y_1}{100}=\frac{9y_1}{20}$
$\Rightarrow 3x=y_1+\frac{9y_1}{20}$
$\Rightarrow \frac{29y_1}{20}=3x$
$\Rightarrow y_1=\frac{20\times 3x}{29}$
$=\frac{60x}{29}$
For the year 2003,
$50=\frac{4x-y_2}{y_2}\times 100$
$\Rightarrow y_2=8x-2y_2$
$\Rightarrow 3y_2=8x$
$\Rightarrow y_2=\frac{8x}{3}$
$\therefore \frac{y_1}{y_2}=\frac{\frac{60x}{29}}{8x}$
$=\frac{60x}{29}\times \frac{3}{8x}=\frac{45}{58}$