Question

A fraction becomes 9/11
if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and denominator it becomes 5/6 Find the fraction.
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Answer 1

Answer:

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Answer 2

Answer:

7 / 9

Step-by-step explanation:

Let numerator be ' a ' and denominator be ' b '

Fraction = a / b

Case 1 :

[ When 2 is added to both fraction become 9 / 11 ]

= > ( a + 2 ) / ( b + 2 ) = 9 / 11

= > 11 a + 22 = 9 b + 18

= > 9 b = 11 a + 4   .... ( i )

Multiply by 5 we get :

= > 45 b = 55 a + 20 ... ( iii )

Case 2 : [ When 3 is added to both fraction become 5 / 6 ]

= > ( a + 3 ) / ( b + 3 ) = 5 / 6

= > 6 a + 18 = 5 b + 15

= > 5 b = 6 a + 3    .... ( ii )

Multiply by 9 we get :

= > 45 b = 54 a + 27 ... ( iv )

From ( iii )  and  ( iv ) we get :

55 a + 20 = 54 a + 27

= > a = 7

Putting a = 7 in ( i ) we get :

9 b = 11 a + 4   [ a = 7 ]

= > 9 b = 77 + 4

= > b = 81 / 9

= > b = 9

Therefore , required fraction is 7 / 9 !