A fraction becomes 9 11 if 2 is added

Asked by admin @ 13/08/2021 in Math viewed by 435 People

A fraction becomes 9/11 if 2 is added to both numerator and denominator. if 3 is added to both numerator and denominator it becomes 5/6 find the fraction by substitution method

Answered by admin @ 13/08/2021

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

A fraction becomes 9 11 if 2 is added

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