Question

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

Answer 1

Let the Unknown number at the numerator be x.

The fraction shall be,

$\frac{x}{x + 5}$

Now, According to the question ;

$\frac{x + 11}{x + 5 - 14} = 5$

Now, we shall solve this linear equation in one variable.

$\frac{x + 11}{x + 5 - 14} = 5 \\ \\ \\ \implies \frac{x + 11}{x - 9} = 5 \\ \\ \\ \implies x + 11 = 5(x - 9) \\ \\ \\ \implies x + 11 = 5x - 45 \\ \\ \\ \implies x + 11 + 45 - 5x = 0 \\ \\ \\ \implies 56 - 4x = 0 \\ \\ \\ \implies 4x = 56 \\ \\ \\ \implies x = 56 \div 4 \\ \\ \\ \implies \boxed{x = 14}$

Hence the fraction is ,

$\frac{x}{x + 5} = \frac{14}{19} (ans)$

Answer 2

Let numerator = x

Then denominator = x + 5

Then, the fraction will be

$\frac{x}{x+5}$

___________________

According to the question,

$\frac{x +11}{x + 5 - 14}$ = 5

5x - 45 = x + 11

4x = 56

x = 14

Denominator = x + 5 = 19

_________________

Hence, fraction is

$\boxed{\huge{\frac{14}{19}}}$