Additional Police Commissioner Ashok Gupta said Payal, a student of Class VIII, went missing on Wednesday and the next day, her body was found near an under-construction school boundary.
When the police reached the spot and questioned the school authorities as well as a few students, they were informed that the two girls had a fight over a pen during their exam a few days back.
"Again on Wednesday, the two had a fight as the accused had taken a pen from Payal who was taunted by her her friends. The accused in return had allegedly abused Payal.
Payal, however, completed her exam silently and went to her home, police said.
Upset at being abused, she went to the accused's residence where she was alone and a fight ensued, police said.
The accused allegedly hit Payal with an iron rod, killing her. She then dragged her body to the basement.
The police said she narated the whole incident to her mother and brother who discovered the body in the basement. "The two sympathised with her and threw Payal's body into a pond after attaching it to a stone," said the police.
The mother reportedly told her husband about the sequence of events, who brought the body out of the pond and threw it near shrubs, fearing her daughter would be cursed if Payal's last rites were not performed, police said.
Meanwhile, police managed to trace the body from there.
The accused has been detained and is in police custody while her parents and brothers have been arrested, said Additional Police Commissioner Ashok Gupta.
( With inputs from IANS )