SSC CGL Model Paper 20

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Question : 63 of 100

Marks: +1, -0

A fraction is greater than its reciprocal by

(72)/(7 7 )

. What is the fraction ?

$7/11$
$11/7$
$4/7$
$7/4$

Solution:

Let the fraction be

x/y

.
According to the question,

x/y=72/77+y/x

⇒

x/y-y/x=72/77

⇒

{x^2-y^2}/{xy}=72/77

⇒

7 7 x ^2 - 7 7 y ^2 = 7 2 x y

⇒

77x ^2 - 72xy - 77y ^2 = 0

⇒

77x ^2 -1 2 1 xy + 49xy - 77y^ 2= 0

⇒

11x ( 7 x - 11 y ) + 7y( 7 x - 11 y ) = 0

⇒

( 7 x - 11y ) (11 x + 7 y ) = 0

⇒

( 7 x - 11y ) = 0 ⇒ 7x =11 y

∴

x/y=11/7

⇒

( 11 x + 7 y ) = 0

⇒

11 x = - 7 y

∴

x/y=-7/11

(not valid)
So,

x/y=11/7

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