Question

The numerator of a fraction is 8 less than the denominator. If the numerator is increased by 17 and the denominator is decreased by 1, the new fraction obtained is 3/2. Find the fraction

Answer 1

Let the denominator =x
Numerator=x-8
Fraction =(x-8)/x----(1)
If the numerator be increased by 17 and denominator. Is decreased by 1=3/2
(x-8+17)/(x-1) =3/2
(x+9)/(x-1)=3/2

2(x+9)=3(x-1)
2x+18=3x-3
18+3=3x-2x
21=x
x=21
Therefore
Fraction = (x-8)/x
=(21-8)/21
=13/21

Answer 2

Let the fraction be x/y, then ;

x=y-8

[(y-8)+17]/(y-1) = 3/2
(y+9)×2 = 3×(y-1)
2y + 18 = 3y - 3
y = 21

then x = y-8
x = 21-8
x = 15

the required fraction is ;
x/y = 13/21

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