Assume that, mass m₁ is greater than mass m₂, so the heavier mass m₁ is accelerating downward and the lighter mass m₂ is accelerating upwards.

For mass $${m_1}$$ the equation will be

$${m_1}$$$$g-T=$$$${m_1}$$$$a$$

For mass $${m_2}$$ the equation will be

$$T-$$$${m_2}$$$$g=$$$${m_2}$$$$a$$

Adding those equations we get

$$a = {{\left( {{m_1} - {m_2}} \right)g} \over {{m_1} + {m_2}}}$$

$$\therefore$$ $${g \over 8} = {{\left( {{m_1} - {m_2}} \right)g} \over {{m_1} + {m_2}}}$$

$$ \Rightarrow {1 \over 8} = {{{{{m_1}} \over {{m_2}}} - 1} \over {{{{m_1}} \over {{m_2}}} + 1}}$$

$$ \Rightarrow$$ $${{{m_1}} \over {{m_2}}} + 1 =$$ $${8\left( {{{{m_1}} \over {{m_2}}} - 1} \right)}$$

$$ \Rightarrow$$ $${{{m_1}} \over {{m_2}}} = {9 \over 7}$$