The children, in the age group of 7 to 16, hailed from tribal-dominated southern districts of Gajapati, Kandhamal and Rayagada.
They were rescued by police with the help of 'Childline', Berhampur, activists from the village on Friday evening. The children are now in the custody of 'Childline', police said.
While 16 of the rescued children were from Mohana area of Gajapati district, 10 were from Bramhanigaon area of Kandhamal district. Three others were from Kenduguda area of Rayagada district, sources said.
The two have allegedly collected Rs 3,500 from the parents of each child for the purpose. The children, however, were yet to join any school and were housed in a single room without proper facilities, police said.
They were arrested on charges of cheating and under various sections of Juvenile Justice Act (JJA), based on a complaint lodged by Prabhu Prasad Patra, a Childline activist, the inspector said.