SSC CGL 17 Aug 2017 Shift 1 Paper

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Question : 63 of 100

Marks: +1, -0

The sum of a fraction and 7 times its reciprocal is

11/2

. What is the fraction ?

$7/2$
$2/7$
$3/4$
$4/3$

Solution:

Let the fraction

= {x}/{y}

and its reciprocal =

y/x

According to the question,

{x}/{y}+7 ×{y}/{x}= {11}/{2}

⇒

{x^{2}+7 y^{2}}/{x y}= {11}/{2}

⇒

2 x^{2}+14 y^{2}=11 x y

⇒

2 x^{2}-11 x y+14 y^{2}=0

⇒

2 x^{2}-4 x y-7 x y+14 y^{2}=0

⇒

2 x(x-2 y) -7 y(x-2 y)=0

⇒

(x-2 y)(2 x-7 y)=0

∴

{x}/{y}= {2}/{1}, {7}/{2}

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