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Step-by-step explanation:

[tex]let \: fraction \: be \: \frac{x}{y} \\ according \: to \: question \: \\ \frac{x}{y + 4} = \frac{1}{2} \\ cross \: multiplication \\ 2x = y + 4 \\ 2x - y = 4\: \: .....(1) \\ \frac{x - 5}{y} = \frac{1}{8} \\ again \: cross \: multiplication \\ 8(x - 5) = y \\ 8x - 40 = y \\ 8x - y = 40 \: \: .....(2) \\ subtracting \: (1) \: from \: (2) \\ 8x - y - (2x - y) = 40 - 4 \\ 8x - y - 2x + y = 36 \\ 8x - 2x = 36 \\ 6x = 36 \\ x = \frac{36}{6} \\ x = 6 \\ putting \: value \: of \: x \: in \: equation \: (1) \\ 2x - y = 4 \\ 2 \times 6 - y = 4 \\ 12 - y = 4 \\ - y = 4 - 12 \\ - y = - 8 \\ y = 8 \\ hence \: fraction \: will \: be \: \frac{x}{y} = \frac{6}{8} [/tex]