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?

10:29

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20:29

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9:10

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21:26

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None of these

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Solution

The correct option is E None of these
Let the expenditures of companies A and B in 2003 be Rs 4x and Rs 5x respectively. If their respective incomes be $I_{1}$ and $I_{2}$ , then for company A,
$45 = \frac{I_{1} - 4 x}{4 x} \times 100$
$\Rightarrow I_{1} - 4 x = \frac{45 x}{25} = \frac{9 x}{5}$
$\Rightarrow I_{1} = \frac{9 x}{5} + 4 x = \frac{29 x}{5}$
For company B,
$50 = \frac{I_{2} - 5 x}{5 x} \times 100$
$\Rightarrow I_{2} - 5 x = \frac{50 x}{20} = \frac{5 x}{2}$
$\Rightarrow I_{2} = 5 x + \frac{5 x}{2} = \frac{15 x}{2}$
$= 29 x$
$∴ \frac{I_{1}}{I_{2}} = \frac{5}{15 x} = \frac{29 x}{5} \times \frac{2}{15 x} = \frac{58}{75}$

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