Question

a fraction becomes 9/11,if 2is added to both the numerator and denomonator .if 3is added to both the numerator and denominator it becomes 5/6 find fraction
sole by substitution method ​

Answer 1

Given :-

▪ A fraction becomes 9/11 , if 2 is added to both the numerator and denominator.

▪ If 3 is added to both the numerator and denominator, it becomes 5/6.

To Find :-

▪ The fraction

Solution :-

Let the fraction be x / y where x and y are numerator and denominator respectively.

Case 1 :

☞ If 2 is added to both the numerator and denominator, the fraction becomes 9/11.

⇒ (x + 2) / (y + 2) = 9/11

⇒ 11x + 22 = 9y + 18

⇒ 11x - 9y = -4

⇒ x = (9y - 4) / 11 ...(1)

Case 2 :

☞ If 3 is added to both the numerator and denominator, the fraction becomes 5/6.

⇒ (x + 3) / (y + 3) = 5/6

⇒ 6x + 18 = 5y + 15

⇒ 6x = 5y - 3

Substituting value of x from (1),

⇒ 6 × (9y - 4) / 11 = 5y - 3

⇒ 54y - 24 = 55y - 33

⇒ 55y - 54y = 33 - 24

⇒ y = 9

Now, y = 9 in (1),

⇒ x = (9×9 - 4) / 11

⇒ x = (81 - 4) / 11

⇒ x = 77 / 11

⇒ x = 7

Hence, The fraction is 7 / 9.

Answer 2

Step-by-step explanation:

suppose numerator is x and denominator is y.

then according to question

x+2/y+2 = 9/11

11x+22 = 9y+18

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

and

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

6x+18 = 5y+15

6x = 5y-3

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

putting value of x in equation 1

then

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

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

55y-33-54y = -24

y = 33-24

y = 9

putting the value of y in equation (2)

x = (5*9-3)/6

x = 45-3/6

x = 7

then the fraction is 7/9

putting the value of x in equation (2)

then,