Data Interpretation Ques 249

Question-

Directions : Study the following table and answer the questions that follow.

The incomes of company $X$ and $Y$ in 2010 were in the ratio of 3 : 4 respectively. What was the respective ratio of their expenditures in 2010?

(1) $7: 22$

(2) $14: 19$

(3) $15: 22$

(4) $27: 35$

(5) $35: 49$

Show Answer

Correct Answer: (3)

Solution: (3)

Income of company X Rs. = Rs. $3 x$ (let)

Income of company Y Rs. $=$ Rs. $4 x$

$\therefore$ Gain per cent $=\left(\frac{\text { Income }- \text { Expenditure }}{\text { Expenditure }}\right) \times 100$

For company X,

$65=\left(\frac{3 x-y_{1}}{y_{1}}\right) \times 100$

$\Rightarrow 65 y_{1}=300 x-100 y_{1}$

$\Rightarrow 165 y_{1}=300 x$

For company Y,

$50=\left(\frac{4 x-y_{2}}{y_{2}}\right) \times 100$

$\Rightarrow 50 y_{2}=400 x-100 y_{2}$

$\Rightarrow 150 y_{2}=400 x$

$\therefore \frac{165 y_{1}}{150 y_{2}}=\frac{300 x}{400 x}=\frac{3}{4}$

$\Rightarrow \frac{y_{1}}{y_{2}}=\frac{3}{4} \times \frac{150}{165}=15: 22$

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