Hi,
In your product you can just enter the price without VAT and select the "default tax category".
Then, you need to create two tax rates via the "manage tax rates" button of the System->Taxation menu for each one of your rate.
Note that both rates will be calculated on the price without VAT, so your second rate needs to be adjusted to take that into account. So instead of having 12.36% you should have a rate of 12.9775%
Then, you create two tax rules via the new button of the System>Taxation menu, one per rate, and you set the zone (India) and the tax category and you publish it.
Finally, when the user will enter his address on the checkout the taxes will be applied or not based on the address. If you want the taxes to be applied by default, you can change the "main tax zone" option of the configuration so that it is India and that the taxes are even applied before the user enter his address.