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UPSC 2014 CDS II Math Paper

Question : 23 of 100

Marks: +1, -0

(x + y) : (x - y) = 3 : 5

and xy = positive imply that

[2014 CDS-II]

x and y are both positive
x and y are both negative
one o f them is positive and one of them is negative
no real solutions for x and y exist

Validate

Solution:

\frac{x+y}{x-y} = \frac{3}{5} \Rightarrow 5x+5y=3x-3y

\Rightarrow 2x = -8y \Rightarrow x = -4y

Therefore, either x is positive and y is negative or x is negative and y is positive. But, it is given that xy is positive. This is not possible as x and y cannot be simultaneously positive or negative.

Thus, there exists no real solutions for x and y

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