Tasneem (50) and her daughter Shibli were rushed to Ursula Horsman Memorial Hospital, where their condition was stated to be critical, a police spokesman said.
The mother-daughter duo sprinkled kerosene and set themselves ablaze outside the district collectorate.
One Jubeida Khan and her family had been staying as a tenant in Tasneem's residence in Chamanganj area for the past 40 years, he said adding, for past some time she had been trying to get back the possession of the house.
Few days back, the belongings of Jubeida and her family were removed from the house with the help of local police, Tasneem's son Zafar Hayat Hasmi told reporters.
However, she managed to occupy the house again, he said.
According to Hasmi, his mother had submitted an application with the district magistrate office but no action was taken in this regard.
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City Magistrate Avinash Singh said that the incident was an outcome of a dispute between the landlord and tenant.
The matter was being investigated and action would be taken against the guilty persons, he said.