Question

a fraction becomes 9/ 11 if 2 is added to both the numerator and the denominator if 3 is added to both numerator and denominator it's become 5/6 find the fraction

Answer 1

Let numerator be x and denominator be y.

If 2 is added to both numerator and denominator, the fraction becomes 9/11.
x+2/y+2 = 9/11
11(x+2) = 9(y+2)
11x+22 = 9y+18
9y-11x = 22-18
9y - 11x = 4
9y = 4+11x
y = (4+11x)/9

If 3 is added to both numerator and denominator, the fraction becomes 5/6.
x+3/y+3 = 5/6
6(x+3) = 5(y+3)
6x+18 = 5y+15
5y = 6x+18-15
5y = 6x+3
y = (6x+3)/5
(4+11x)/9 = (6x+3)/5
5(4+11x) = 9(6x+3)
20+55x = 54x + 27
55x-54x = 27-20
x = 7

y = (4+11(7))/9 = (4+77)/9 = 81/9 = 9
Therefore, x = 7 and y = 9
The fraction = 7/9

Hope it helps

Answer 2

Answer:

Fraction = 7 / 9 .

Step-by-step explanation:

Let the numerator of fraction be x and denominator be y .

Friction = x / y

First case : [ When 2 added in both ]

x + 2 / y + 2 = 9 / 11

11 x + 22 = 9 y + 18

11 x - 9 y = - 4  ... ( i )

Second case : [ When 3 added in both ]

x + 3 / y + 3 = 5 / 6

6 x + 18 = 5 y + 15

6 x - 5 y = - 3 ... ( ii )

Now Multiply by 6 in ( i ) and by 11 in ( ii )

66 x - 54 y = - 24

66 x - 55 y = - 33

-      +            +           [ Subtracting ( ii )  from  ( i )  ]

               y = 9

Now x = - 4 + 9 y / 11  ... ( i )  [ y = 9 ]

x = 77 / 11

= > 7

Now we have x = 7 and y = 9

Thus , fraction is 7 / 9 .