# 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.

2
by dweejareddy

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by dweejareddy

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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

give that the fraction will become 4/5 if 1 is added to numerator and denominator

so

4/5 =(p+1)/(q+1)

4q+4 = 5p+5

and

(p-5)/(q-5)=1/2

2p-10=q-5

q= 2p-5

SO

4(2p-5) +4 =5p+5

8p-20+4 = 5p+5

3p= 21

p=7

Therefore q=2*7-5

q=9

So the fraction is 7/9