Tenant pays advance to shift and changes mind after a week

Hi.. I have a situation here. I have a flat in Hyderabad which I wanted to rent out and posted an ad in a newspaper on 30th May. I received multiple inquiries and I closed the deal with one person on the 1st and took an advance of 1 month rent. The tenant said they would shift by the 5th. The tenant requested us to get the house painted even though the house was painted just a few months back. We agreed and got the house renovated by 3rd June and we informed the tenant about the same. The tenant agreed to shift. On 6th June the tenant calls us and tells us that they found a cheaper house and so do not want to take this house on rent and demanded their money back. They suggested I post an another ad and get a new tenant and asked us to deduct the ad money and 10 days rent. I still did not get a new tenant for my house as most of the tenants usually shift houses at the beginning of the month. I now have to bear ad fees again, maintenance and electricity bill for the current month. Should I pay anything back to them legally? SInce they cheated us by putting us on hold and finding a cheaper option. PS: No agreement was signed. Your advice will be really helpful in this regard. Thank you, Sajid