Tenant not vacating (No rent agreement)

Hello, We gave our first floor on rent to a lady (divorcee) and her daughter in month of January. My mother stays on ground floor alone. I work in Delhi. I had asked my mother to get the rent agreement created but she said the lady doesn't look like a reliable tenant and it's better to make sure she leaves so she didn't get the rent agreement created even due to my repeated appeals. Now my mother wants to move to Delhi with me and we don't want to keep this tenant in our house as she doesn't maintain the house properly and she has a bad attitude as she always talks to my mother angrily. Now my mother has been asking the tenant to vacate the house from April she keeps on moving the date by giving reasons such as her daughter's exams are there so she kept asking for extension. Now it's July and she had told us that she would vacate today i.e. 25th July 2015. But today when we had a discussion she said she is not able to find a house for rent according to her choice and can't vacate. She has been saying the same thing from last 2 months. She is not claiming ownership of the house and pays regular rent but we can't keep the house alone with her because she doesn't know how to maintain it. Please let me know what can we do in this case. Thanks.