Question

a faction 9/11 , if 2 is added to both the numerator and the denominator.
11
If, 3 is added to both the numerator and the denominator it becomes 5/6
. Find the
fraction.​

Answer 1

Answer:

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=-3×11

or, y+24=33

or, y=33-24=9

then, x=(9×9-4)/11

or, x=(81-4)/11

or, x=77/11=7

∴, x=7,y=9 and the fraction is :7/9

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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.