Question

A fraction becomes 9 upon 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 upon 6 . Find the fraction.

find this answer please in proper way

Answer 1

Answer:

Step-by-step explanation:

Numerator=x

Denominator=y

Fraction=x/y

x+2/y+2=9/11

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

11x+22=9y+18

11x-9y=18-22

11x-9y=-4..........1st equation

x+3/Y+3=5/6

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

6x+18=5y+15

6x-5y=15-8

6x-5y=-3

6x=-3+5y

x=-3+5y/6

From equation 1

11x-9y=-4

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

-33+55y/6 -9y=-4

-33+55y-54y/6=-4

-33+y=-24

y=-24+33

y=9

x=-3+5y/6

x=3+5×9/6

x=-3+45/6

x=42/6

x=7

The fractionx/y=7/9

Answer 2

Answer:

Let the numerator and denominator be x and y respectively.

Therefore, the required fraction will be x/y

According to Question now,

➳ (x + 2)/(y + 2) = 9/11

➳ 11(x + 2) = 9(y + 2)

➳ 11x + 22 = 9y + 18

➳ 22 - 18 = 9y - 11x

➳ 4 = 9y - 11x

➳ 11x = 9y - 4

➳ x = 9y - 4/11.......[Equation (i)]

Now, it is given that 3 is added to both numerator and denominator it becomes 5/6 :]

➳ (x + 3)/(y + 3) = 5/6

➳ (x + 3)6 = 5(y + 3)

➳ 6x + 18 = 5y + 15

➳ 6x - 5y + 18 - 15 = 0

➳ 6x - 5y + 3 = 0

➳ 6(9y - 4)/11 - 5y + 3 = 0

➳ 54y - 24/11 = 5y - 3

➳ 54y - 24 = 11(5y - 3)

➳ 54y - 24 = 55y - 33

➳ -24 + 33 = 55y - 54y

➳ 9 = y

Now, Putting y = 9 in equation (i) we get,

➳ x = 9y - 4/11

➳ x = 9(9) - 4/11

➳ x = 81 - 4/11

➳ x = 77/11

➳ x = 7

Therefore, the required fraction is 7/9.