Question

the denominator of a rational number is Greater then its number by 8 if numerator is increased by 17 and denominated is decrease bye by a 1, the number obtain is 3 /2 the rational number is

Answer 1

let the numerator be x
the denominator will be x+8
rational number=x÷x+8

Answer 2

LET THE RATIONAL NUMBER BE a/b
GIVEN DENOMINATOR IS GREATER THAN THE NUMERATOR BY 8
⇒b=a+8
IF NUMERATOR IS INCREASED BY 17 AND DENOMINATOR IS DECREASED BY 1,THE NUMBER BECOMES 3/2
⇒a+17/b-1=3/2
BUT b= a+8
⇒a+17/(a+8)-1=3/2
a+17/a+7=3/2
⇒2a+34=3a+21
⇒a=34-21=13 ⇒ a=13
SUBSTITUTING a=13 IN b=a+8
⇒b=21 
∴THE RATIONAL NUMBER IS 13/21