Question

the denominator of a fraction is greater than the numerator by 8.if the numerator is increased by 17 and denominator is decreased by 1,the number obtained is 3/2,find the fraction

Answer 1

Heya !!



Let numerator of fraction be X.


Denominator = ( X + 8 )



Fraction = Numerator/Denominator = X/X+8



According to the question,



X + 17 / X + 8 - 1 = 3/2



X + 17 / X + 7 = 3/2



2 ( X + 17 ) = 3 ( X + 7 )



2X + 34 = 3X + 21



3X - 2X = 34 - 21



X = 13



Numerator = X = 13


And,


Denominator = X + 8 = 13+8 = 21



Fraction = 13/21.

Answer 2

hey!!!

ATQ, the denominator of a fraction is greater than the numerator by 8.

let the numerator of the fraction be x. therefore the denominator of the fraction is x + 8

if the numerator is increased by 17 and denominator is decreased by 1, then the number obtained is 3/2

therefore x+17/(x+8)-1 = 3/2
>> x+17/x-7 = 3/2
>> 2(x+17) = 3(x-7)
>> 2x + 34 = 3x - 21
>> 34 + 21 = 3x - 2x
>> 13 = x

hence, the numerator of the fraction is = x = 13
and denominator = x + 8 = 13 + 8 = 21

verification :-

= 13 + 17/ 21 - 1
= 30/20
= 3/2

hence verified!

final answer - 13/21

cheers!!!