SSC CPO SI and ASI 2016 Paper

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Question : 108 of 200

Marks: +1, -0

If

3^{x+y}=81

and

81^{x-y}=3,

then the value of

x/ y

is

$17 /15$
$15/ 34$
$15/ 17$
$17/ 30$

Solution:

(1)

3^{x+y}=81=3^{4}

⇒ x+y=4. .................(1)

And,

3^{4(x-y)}=3^{1}

⇒ x-y={1}/{4}..................(2)

Combining equations (1) and (2),
we get,

x={1}/{2}(4+{1}/{4})={17}/{8}

y=4-{17}/{8}={15}/{8}

Hence,

{x}/{y}={{17}/{8}}/{{15}/{8}}={17}/{15}

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