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:

here is your answer

Step-by-step explanation:

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Answer 2

Answer:

The fraction is 7/9

Step-by-step explanation:

Let the fraction be x/y

Now, according to the Question,

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

Cross multiplying we get,

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

11x + 22 = 9y + 18

11x + 22 - 9y = 18

11x - 9y = 18 - 22

11x - 9y = -4 ------- 1

Now, according to the Question,

(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 -------- 2

We have eq.1 and eq.2

Using Substitution method,

Now, from eq.2

6x - 5y = -3

6x = 5y - 3

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

Putting eq.3 in eq.1 we get,

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

((55y - 33)/6) - 9y = -4

Taking LCM = 6

((55y - 33)/6) - 9y × (6/6) = -4

((55y - 33)/6) - (54y/6) = -4

Taking denominators common,

(55y - 33 - 54y)/6 = -4

(55y - 54y - 33)/6 = -4

(y - 33)/6 = -4

y - 33 = -4 × 6

y - 33 = -24

y = 33 - 24

y = 9

Putting y = 9 in eq.3 we get,

x = (5(9) - 3)/6

x = (45 - 3)/6

x = 42/6

x = 7

Hence,

the fraction x/y = 7/9

We can also check this,

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

9/11 = 9/11

Hence it is correct.

also,

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

10/12 = 5/6

Reducing the fraction,

5/6 = 5/6

Hence it is also correct

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