GATE CSE 2024 | Set 1 | GA: 2

Question

​​​If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\frac{x}{y}$

• A. depends on $x y$
• B. depends only on $x$ and not on $y$
• C. depends only on $y$ and not on $x$
• D. is a constant

Answer 1

Given that, $(x+y) = \text{K} (x-y)$

$\Rightarrow x + y = \text{K}x - \text{K}y$

$\Rightarrow y + \text{K}y = \text{K}x -x$

$\Rightarrow x(\text{K} -1) = y(\text{K} + 1)$

$\Rightarrow \dfrac{x}{y} =  \dfrac{(\text{K} + 1)}{(\text{K} -1)}$

$\Rightarrow \dfrac{x}{y} = \text{Constant}$

Correct Answer: D

Comments

What if k = 1, then how it's a constant. as 2/0 = infinity.

And if we do (x+y)/(x-y) then whatever value we will take for x we can't take the same value for y as then x-y will be 0. Therefore why not the answer is c.

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@TusharRana 

You can't take $K=1$ because then initial $(x+y) =K(x-y)$ makes $y=0$ but it is given that x and y are two distinct non-zero real variables.

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Okay got it. But how to think in a way that yield these correct answers. As I mentioned in the comment above why my approach is wrong in the first place?

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You have given $(x+y)=K(x-y)$ and you need $x/y$. So, you need to divide the whole equation by $x$ or $y$ and it is already given that x and y are non-zero so there will be no issue while dividing by x or y.

x is not equal to y is given so that you will not get $K= \infty$ and you have already mentioned the issue with $K=1$ because $K-1$ is in the denominator of $x/y.$  .