Question

The incomes of the Companies X and Y in 2000 were in the ratio of 3 : 4 respectively. What was the respective ratio of their expenditures in 2000?

• A. 14 : 19
• B. 15 : 22
• C. 27 : 35
• D. 33 : 40

Answer 1

The correct option is B

15 : 22

Let the incomes in 2000 of Companies X and Y be 3x and 4x respectively.

And let the expenditures in 2000 of Companies X and Y be E${}_1$ and E${}_2$ respectively.

Then, for Company X we have :

$\begin{array}{cc}65=\frac{3x-E_1}{E_1}\times 100\Rightarrow \frac{65}{100}=\frac{3x}{E_1}-1\Rightarrow E_1=3x\times \left(\frac{100}{165}\right)& ...\left(i\right)\\ ForCompanyYwehave:& \\ 50=\frac{4x-E_2}{E_2}\times 100\Rightarrow \frac{50}{100}=\frac{4x}{E_2}-1\Rightarrow E_2=4x\times \left(\frac{100}{150}\right)& ...\left(ii\right)\\ From\left(i\right)and\left(ii\right),weget:\frac{E_1}{E_2}=\frac{3x\times \left(\frac{100}{165}\right)}{4x\times \left(\frac{100}{150}\right)}=\frac{3\times 150}{4\times 165}=\frac{15}{22}& \end{array}$