Cost for interior designing to 2BHK in Chennai:

Interior of any space is defined by its look and requirements. You need to list out your requirements. Then how much budget you want to share to a specific area. Generally people prefer to spend a little bit more on drawing room and kitchen.
Let me assume your house is 2BHK. To design a 2BHK house in Chennai, you may need to do some electrical work, may be some plumbing works, false ceiling, furniture, painting, furnishing, some glass work and some decorative elements too may come in the house. 
Now 2BHK consist of 2 Beds, two dressing units, two wardrobes, may be one or two TV units, a fully designed kitchen and one or two study tables. For this amount of furniture and interior work, you need to spend around 8 to 10 lacks or rupees minimum. You can drag this amount to infinite figure too. :)
If you hire a good designer and ask him to finish the project in the tight budget, that would be beneficial to you. Some times designers work out lovely things in tight budgets