Question

the denominator of a rational number is greater than its numerator by 5. if the numerator is increased by 11 and denominator is decreased by 14,the new number becomes 5.find the original rational number.

Answer 1

Let the numerator be x, then denominator is x+5 :
$\frac{x}{x + 5}$
According to the question,
$\frac{x + 11}{x + 5 - 14} = 5$
$\frac{x + 11}{2x - 14} = 5$
x+11=5(2x-14)
x+11=10x-70
11+70=10x-x
81=9x or 9x=81
$x = \frac{81}{9} = 9$
x=9
Therefore, denominator is x+5=9+5=14
Original rational no.=
$\frac{9}{14}$
Please let me know if this is the right answer.