Question

the numerator of a fraction is 6less than the denomination if 8 is added to the numerator the fraction is equal to 2/3 find the original fraction​

Answer 1

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$let \: the \: fraction \: be \: \frac{x}{y} \\ from \: given \: \\ y - 6 = x - - (1)\\ \frac{x + 8}{y} = \frac{2}{3} -- (2) \\ solving \: the \: first \: we \: get \: value \: of \: x = y - 6 \: \\ we \: put \: it \: in \: the \: second \: equation \\ \frac{(y - 6) + 8}{y} = \frac{2}{3} \\ \frac{y + 2}{y} = \frac{2}{3} \\ 3y + 6 = 2y \\ 3y - 2y = - 6 \\ y = - 6 \\ put \: value \: of \: y \: in \: (1) \\ x = y - 6 \\ x = - 6 - 6 \\ x = - 12 \\ therefore \: the \: fraction \: is \: \frac{ - 12}{ - 6} = \\ \frac{12}{6}$

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