You can claim income tax exemption on both house rent allowance (HRA) and repayment of housing loan. If you are living in a rented house and paying home loan on another property - even if both the properties are located in the same city - you can claim tax benefit.

Salaried individuals who live on rent can claim HRA to lower their taxes. It is partially exempted. However, if the individual does not live in a rented accommodation, HRA is fully taxable. 

Read more - Can You Claim Both HRA And Home Loan For Tax Exemption?