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:

let the numerator be x

and, denominator be y

Required fraction = x/y

ATQ,

x+9/y+9=9/11

CROSS-MULTIPLYING;

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

11x+99=9y+81

11x-9y=18-------(i).

AND,

x+3/y+3=5/6

CROSS-MULTIPLYING;

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

6x+18=5y+15

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

Multiplying eq.(i). by 5 , and

Multiplying eq.(ii). by 9 .

55x-45y=90-------(iii).

54x-45y=-27------(iv).

subtracting eq.(iii) and eq.(iv).

55x-45y=90

54x-45y=-27

- + +

x=63

y=27

HOPE IT HELPS...........