BERT-like language models (LMs), when exposed to large unstructured datasets, are known to learn and sometimes even amplify the biases present in such data. These biases generally reflect social stereotypes with respect to gender, race, age, and others. In this paper, we analyze the variations in gender and racial biases in BERT, a large pre-trained LM, when exposed to different demographic groups. Specifically, we investigate the effect of fine-tuning BERT on text authored by historically disadvantaged demographic groups in comparison to that by advantaged groups. We show that simply by fine-tuning BERT-like LMs on text authored by certain demographic groups can result in the mitigation of social biases in these LMs against various target groups.