Question

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

Answer 1

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