Question

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

Answer 1

let numerator be x  
∴the denominator will be x+8 
⇒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 
∴x/x+8
=13/21     (Ans  )                                                                                                                          

Answer 2

let  a/b is the fraction,

b-8=a

b=a+8

a+17/b-1=3/2

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

a+17/a+7=3/2

2a+34=3a+21

34-21=3a-2a

13=a


a+8=b
13+8=b

21=b

the fraction is  13/21


hope helped!