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 56. Find the fraction​

Answer 1

Step-by-step explanation:

Let the fraction is x/y. Then by the given

question,

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

or, 11x+22=9y+18 or, 11x-9y-18-22

or, 11x-9y=-4

or, 11x=9y-4

or, x=(9y-4)/11

and, (x+3)/(y+3)=5/6 or, 6x+18=5y+15

or, 6x-5y-15-18 or, 6(9y-4)/11-5y=-3

or, (54y-24-55y)11=-3

or, -y-24=-3x11

or, y+24=33

or, y=33-24-9

then, x=(9x9-4)/11

or, x=(81-4)/11 or, x=77/11=7

.., x=7,y=9 and the fraction is :7/9

Answer 2

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.