They killed themselves in a shanty in Tanavara here Wednesday night, police said.
They said the family, who belonged to Luni near Jodhpur, took the extreme step as it was unable to bear with the poverty and prologued illness of the mother of the two minor children-- all three now dead.
While the bodies of Karnaram Patel (45) and his wife Pushpa (40) were found hanging together by a bar in the roof of the shanty, those of two children-- Urmila (9) and Suresh (7)-- were hanging separately, police said.
"Their bodies were found hanging from the roof of the shanty by the only surviving son in the morning, who informed his uncle, who in return approached the police," said Rajesh Yadav, Station House Officer, Basni.
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The SHO said, "We rushed to the spot and found four bodies hanging, including those of two children."
He said "a bottle of chemical" was also found lying nearby, making police suspect the parents first gave it to the children and hanged them, before taking their own lives.
"A lot of medicines and prescriptions were found in the shanty. Also, Pushpa looked quite weak suggesting she had been undergoing treatment for a long time," Yadav said.
Police have preserved viscera samples and have been awaiting the post-mortem reports.