Question

The fraction becomes 9by 11 if 2is added to both the numerator and the denominator. if 3 is added to both the numerator and the denominator it becomes 5 by 6.find their fraction

Answer 1

Let        Numerator   = xDenominator  = yFraction will              = x/ yA fraction becomes 9/11, if 2 is added to both the numerator and the denominator(x+2)   =          9 y+2               11
Cross multiply we get11 x + 22        = 9y + 18Subtract 22 both side we get11 x     = 9 y – 4Divide 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                6Cross 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         =  -9y         = 9Plug this value of y in equation (1)  we getx               = 9 y – 4     11                                … (1)
x          = (81 – 4)/77x          = 77/11x          = 7