Question

. If 1 is added to both the numerator and the
denominator of a given fraction, it becmoes 4/5. If 5is
subtracted from both the numerator and the
denominator, the fraction becomes 42. Find the
fraction.​

Answer 1

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

Answer 2

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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