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

Let the Numerator be x

Let the Denominator be y Fraction = x/y

According to the Question, ⇒ (x + 2)/y + 2 = 9/11

On Cross multiplying ,

⇒ 11x + 22 = 9y + 18

Subtracting 22 from both sides,

⇒ 11x = 9y – 4

Dividing by 11, we get

⇒ x = 9y – 4/11 … (i)

Then,

⇒ (x+3)/y +3 = 5/6 … (ii)

On Cross multiplying ,

⇒ 6x + 18 = 5y + 15

Subtracting the value of x, we get

⇒ 6(9y – 4 )/11 + 18 = 5y + 15

Subtracting 18 from both the sides

⇒ 6(9y – 4 )/11 = 5y – 3

⇒ 54 – 24 = 55y – 33

⇒ –y = – 9

⇒ y = 9

Putting this value of y in equation (i), we get

⇒ x = 9y – 4

⇒ x = (81 – 4)/77

⇒ x = 77/11

⇒ x = 7

Hence, the fraction is 7/9.

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