Question

A fraction becomes 9/11 if 2 is added to both numerator and the denominator, it becomes 5/7 if 2 is subtracted from both numerator and the denominator. Find the fraction.

Answer 1

$\huge\mathbb{\underline{Answer:-}}$

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