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

Answer:

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

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

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

Hence, the fraction is 7/9.

Answer 2

Step-by-step explanation:

Putting tha value of y in eq. i

11x-9y=-4

11x-9 × 9 = - 4

11x - 81 = -4

11x = -4 + 81

11x = 77

x = 77/11

x = 7

HENCE x ( numerator ) = 7

y( denominator ) = 9