Question

the denominator of a rational number is greaten then it's numerator by 3 if three is subtracted from the numerator and 2 is added a 2 it's denominator the new number becomes 1/5 find the orginal number

Answer 1

Let the numerator of the original fraction be x and the denominator of the original fraction be ( x + 3 ) ,





Given in the question that 3 subtracted from numerator and 2 added to the denominator, new fraction becomes 1 / 5


Converting the theory in equation,



$= > \frac{x - 3}{x + 3 + 2} = \frac{1}{5} \\ \\ \\ = > \frac{ x- 3}{x +5 } = \frac{1}{5} \\ \\ \\ = > 5(x - 3) =x + 5 \\ \\ \\ = > 5x - 15 = x + 5 \\ \\ \\ = > 5x - x = 5 + 15 \\ \\ \\ = > 4x = 20 \\ \\ \\ = >x = \frac{20}{4} \\ \\ \\ = > x = 5$




Hence,


Original fraction = x / ( x + 3 )

$\boxed{ \bold{ \: original \: fraction \: = \frac{x}{x + 3} = \frac{5}{5 + 3} = \frac{5}{8} }}$

Answer 2

Let numerator of rational number be X.



Denominator = ( X + 3 ).




Fraction = Numerator/Denominator = X/X+3.




According to the question,

X - 3 / X + 3 + 2 = 1/5



X - 3 / X + 5 = 1/5




X + 5 = 5 ( X - 3 )



X + 5 = 5X - 15



5X - X = 20



4X = 20


X = 5.


Numerator of fraction = X = 5


And,


Denominator of fraction = X + 3 = 8




Fraction = Numerator / Denominator = 5/8.