Question

The numerator of a fraction is 6 less than the denominator. If the numerator is reduced by 2 and the denominator is increased by 3, the fraction becomes 3/14. Find the original faction.​

Answer 1

$\blue{\texttt{Given \: that :-}}$

• The numerator of a fraction is 6 less than the denominator.
• If the numerator is reduced by 2 and the denominator is increased by 3, the fraction becomes 3/14.

$\large\underline\blue{\text{To \:  Find :-  }}$

• The original fraction

$\large\underline\purple{\bold{Solution :- }}$

☆ Let denominator of a fraction be x.

☆ So, numerator of a fraction is x - 6

$\tt\implies \: \: fraction \: = \dfrac{x - 6}{x} - - - (1)$

☆ Now, According to statement,

☆ numerator is reduced by 2

$\tt\implies \:numerator \: = x - 6 - 2 = x - 8$

☆ denominator is increased by 3

$\tt\implies \:denominator \: = x + 3$

$\blue{\texttt{Given \: that \: fraction \: = }}\dfrac{3}{14}$

$\tt\implies \:\dfrac{x - 8}{x + 3} = \dfrac{3}{14}$

$\tt\implies \:14x - 112 = 3x + 9$

$\tt\implies \:14x - 3x = 112 + 9$

$\tt\implies \:11x = 121$

$\tt\implies \:x = 11$

$\begin{gathered}\begin{gathered}\bf Hence -  \begin{cases} &\sf{numerator \: = x - 6 = 11 - 6=5 } \\ &\sf{denominator = x = 11} \end{cases}\end{gathered}\end{gathered}$

$\text{Hence, \: fraction } = \: \dfrac{5}{11}$