CAT 2022 Slot 3 Paper

Question : 47 of 66

Marks: +1, -0

If $(√{7/5}) 3x-y = 875/2401$ and $({4a}/b) 6x-y= ({2a}/b) y-6x$ for all non-zero real values of $a$ and $b$ , then the value of $x+y$ is

Solution:

(√{{7}/{5}}) ^{3 x-y}={875}/{2401}

({7}/{5}) ^{{(3 x-y)}/{2}}={125}/{343}

({7}/{5}) ^{{(3 x-y)}/{2}}= ({7}/{5}) ^{-3}

3 {\x}- {\y}=-6

({4 a}/{b}) ^{6 x-y}= ({2 a}/{b}) ^{y-6 x}

Therefor,

y=6 x

as the bases are different so the power should be zero for the results to be equal.

3 x-y=-6

or,

3 x-6 x=-6

{\x}=2

y=6 x=12

x+y=14

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