Question

the denominator of a rational number is greater than its numerator by 7. if the numerator is increased by 19 and the denominator is decreased by3 the new number becomes 4. find the orginal number

Answer 1

Let the numerator of original number = x  
           denominator of original number =  x + 7 


Original Fraction = $\frac{x}{x + 7 }$



According to the question, numerator is increased by 19 and denominator is decreased by 3 

Numerator becomes = (x +  19) 
Denominator becomes = (x + 7 - 3)  = (x + 4)
Fraction becomes = $\frac{x + 19}{x + 4 } = 4$


Now,

$\frac{x + 19 }{x + 4 } = \frac{4}{1}$



1(x + 19) = 4(x + 4) 

x + 19 = 4x + 16

19 - 16 = 4x - x 

3= 3x 

1  = x 



Original Fraction = $\frac{x}{x + 7 } = \frac{1}{1 + 7} = \frac{1}{8}$

Answer 2

Answer of your question is 1/8.