Question

a. The denominator of a rational number is greater than its numerator by 5. If the numerator is
increased by 11 and the denominator is decreased by 14, the new number becomes 5. Find the
original rational number.
​

Answer 1

Explanation:

numerator=x

denominator=x+5

x+11/x+5-14 =5

x+11/x-9=5

x+11=5x-45

4x=56

x=14

x+5=19

original number=14/19

Answer 2

$\sf \implies Let \: the \: numerator \: of \: the \: fraction \: be \: x$

$\sf Then \: according \: to \: question,$

$\sf \implies The \: denominator \: will \: be \: (x+5)$

$\sf \underline{Conditions \: given \: in \: the \: question \: are} :$

If the Numerator is increased by 11 and the Denominator is decreased by 14, then the number becomes 5.

$\sf \underline{Hence, our \: equation \: will \: be} :$

$\red{\implies\bf \dfrac{(x + 11)}{(x + 5 - 14)} = 5}$

$\sf \underline{Now, we \: will \: solve \: the \: above \: equation. }$

$\implies\sf \dfrac{(x + 11)}{(x - 9)} = 5$

$\implies\sf x + 11 = 5x - 45$

$\implies\sf - 4x + 11 = - 45$

$\implies\sf - 4x = - 45 - 11$

$\implies\sf - 4x = - 56$

$\implies\sf x = \dfrac{ - 56}{ - 4}$

$\implies\sf x = 14$

$\sf \underline{Therefore},$

$\implies\sf Numerator \: (x) = 14$

$\sf\implies Denominator \: (x+5) = 14+5 = 19$

$\underline{ \boxed{ \sf \pink{Thus, the \: original \: fraction \: is \: \dfrac{14}{19} } }}$