There are two solutions to this oil burning.
Drain at 8,000 km, use 0w20 or 5w30 API-SN or higher. 4L box will cost 5500 rs. Now, it'll cost you 0.6875 rupees per KM.
Drain at 3000 km with cheap mineral or semi synthetic oil. It should not cost above 3000 rs.
It'll cost you 1 rupee per KM.
So, changing oil at 3000km even with cheap oil will be much more expensive.
0w20 havoline, drain at 8,000km, just keep checking oil after every 1500km.
If you can find super cheap oil and change at 3,000km where it's more economical than changing fully synthetic oil at 8,000km, sure go for it.