A fraction becomes 4 5 if 1 is added

Asked by admin @ in Math viewed by 259 People

A fraction becomes 4/5 if 1 is added to both numerator and denominator . If however, 5 is subtracted from both numerator and denominator, the fraction becomes 1/2. Find the fraction.

Answered by admin @


Let the fraction be x/y
1 is added means
x+1/y+1=4/5
5x+5=4y+4
5x-4y=-1
5 is subtracted means
x-5/y-5=1/2
2x-y=5
2 eqn multilply by 5 and 1 eqn by 2
2(5x-4y=-1)=10x-8y=-2
5(2x-y=5)=10x-5y=25
10x-5y=25
10x-8y=-2
x=7,y=9
then the fraction  is 7/9

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