Tension(T)  is a pull and is the same on both objects

Up is set as the positive direction

Red Object        T - m_redg = m_reda      (it is accelerated upwards thus a is positive)

Purple Object    T - m_purpleg = - m_purplea   (it is accelerated downwards thus a is negative)

Sovle each equation for T

T = m_reda  +  m_redg

T = m_purpleg - m_purplea                  (Set T = T)

  
m_reda  +  m_redg   =   m_purpleg - m_purplea       (Solve for a)

m_reda  +  m_purplea = m_purpleg - m_redg

a (m_red  +  m_purple ) = m_purpleg - m_redg

  
        m_purpleg - m_redg           9.80 m/s² ( 20.0 kg - 10.0 kg )
a = -------------------------- = -------------------------------------------- = 3.27 m/s²
       (m_red  +  m_purple )                ( 10.0 kg  +  20.0 kg)