Question

The incomes of two 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. 7:22
• B. 14:19
• C. 15:22
• D. 27:35

Answer 1

Answer: (C)

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 E1 and E2 respectively.
Then, for Company X we have:
$65=\frac{3x-E_1}{E_1}\times 100\Rightarrow \frac{65}{100}=\frac{3x}{E_1}-1\Rightarrow E_1=3x\times \left(\frac{100}{65}\right)$....(i)
For Company Y we have:
$50=\frac{4x-E_2}{E_2}\times 100\Rightarrow \frac{50}{100}=\frac{4x}{E_2}-1\Rightarrow E_2=4x\times \left(\frac{100}{150}\right)$...(ii)
From (i) and (ii), we get:
$\frac{E_1}{E_2}=\frac{3x\times \left(\frac{100}{165}\right)}{4x\times \left(\frac{100}{150}\right)}=\frac{3\times 150}{4\times 165}=\frac{15}{22}$ (Required ratio).