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

Answer 1

Let the fraction be x/y.

According to the question,

(x + 2)/(y + 2) = 9/11

11x + 22 = 9y + 18

11x – 9y = -4 …………….. (1)

(x + 3)/(y + 3) = 5/6

6x + 18 = 5y +15

6x – 5y = -3 ………………. (2)

From (1), we get

x = (-4 + 9y)/11 …………….. (3)

Substituting the value of x in (2), we get

6[(-4 + 9y)/11] – 5y = -3

-24 + 54y – 55y = -33

-y = -9

y = 9 ………………… (4)

Substituting the value of y in (3), we get

x = (-4 + 81)/11 = 77/11 = 7

Hence, the fraction is 7/9.

Answer 2

Answer:

Step-by-step explanation:

let the numerator be x and denominator be y

x+2/y+2=9/11

=11(x+2)=9(y+2)

11x+22=9y+18

11x-9y= -4  ---------(1)

now,

x+3/y+3=5/6

= 6x+18=5y+15

6x-5y=-3---------------(2)

using elimination method

multiply (1) by 6 and (2) by 11

we get,

      66x-54y= -24

      66x-55y=-33

            y= 9

6x-5×9=-3

6x-45=-3

6x=42

x=7

fraction=7/9