Sunday, March 31, 2013

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 the denominator it becomes 5/6 . Find the fraction.


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 the denominator it becomes 5/6 . Find the fraction.
             
Let        Numerator   = x
Denominator  = y
Fraction will              = x/ y
A fraction becomes 9/11, if 2 is added to both the numerator and the denominator
(x+2)   =          9
 y+2               11

Cross multiply we get
11 x + 22        = 9y + 18
Subtract 22 both side we get
11 x     = 9 y – 4
Divide by 11 we get
 x        = 9 y – 4     
                                                            11                          … (1)
Given that 3 is added to both the numerator and the denominator it becomes 5/ 6.
If, 3 is added to both the numerator and the denominator it becomes 5/6
(x+3)   =          5                      … (2)
 y+3                6
Cross multiply we get
 6x + 18 = 5y + 15
 Subtract the value of x now we get
    6(9 y – 4 )   + 18 = 5y + 15
                                      11                  
Subtract 18 both side we get
 6(9 y – 4 )     = 5y  - 3 
                                    11                   
                       
54   – 24         =  55 y  -  33
-y         =  -9
y         = 9
Plug this value of y in equation (1)  we get
x               = 9 y – 4     
11                                … (1)

x          = (81 – 4)/77
x          = 77/11
x          = 7

Hence our fraction is 7/9

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