Question

A fraction becomes 9by11 if 2 is
added to both
the numerator and
the
denominator of 3
of 3 is added
to both the numberator and the
denominator it
the
fraction,
becomes.
5 by 6 find the fraction​

Answer 1

Answer:

The fraction is 7/9

Step-by-step explanation:

I believe your Question was,

"A fraction becomes 9/11, if 2 is added to both the numerator and the denominator, If 3 is added to both the numberator and the denominator, the fraction becomes 5/6, find the fraction."

Let the numerator be x and denominator be y

So, the fraction is x/y

Now,

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

Cross multiplying we get,

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

11x + 22 = 9y + 18

11x - 9y = 18 - 22

11x - 9y = -4

11x = 9y - 4

x = (9y - 4)/11 ----- 1

Now,

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

Cross multiplying we get,

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

6x + 18 = 5y + 15

6x - 5y = 15 - 18

6x - 5y = -3

Putting x = (9y - 4)/11 in the above equation,

(6(9y - 4)/11) - 5y = -3

((54y - 24)/11) - 5y = -3

Taking 11 as LCM

((54y - 24)/11) - (55y/11) = -3

(54y - 24 - 55y)/11 = -3

(-y - 24)/11 = -3

-y - 24 = -3 × 11

-y - 24 = -33

-y = -33 + 24

-y = -9

y = 9

Now,

Putting y = 9 in eq.1

x = (9(9) - 4)/11

x = (81 - 4)/11

x = 77/11

x = 7

Thus,

the fraction is 7/9

We can also check this,

(7 + 2)/(9 + 2) = 9/11

and

(7 + 3)/(9 + 3) = 10/12 = 5/6

Hope it helped and you understood it........All the best