Will my desktop work in US, given there we have 120 volts supply and here in India we have 220 volts supply in households. I'm open for workarounds as well like a switched-mode power supply change, or something like that.
Without more details about the components in your specific desktop, it is impossible to say for certain, but you can check the labels on the power supply.
Your computer does not, from a certain point of view, run on either 110V or 220V A/C power. The internal components run on DC power— fans and disk drives at +12V, the memory and processors at +3.3V, and so forth. Your computer has a power supply unit which converts the power from the mains to power that the components can use.
Although most portable consumer electronics like mobile phones or notebook computers are sold with a transformer that accommodates common consumer current around the world (100–240V, 50–60 Hz)— this is what is in the "brick" in the power cable— whether or not a desktop (or printer, monitor, or other large peripherals) can handle a certain voltage or frequency depends on whether or not its power supply unit can take the input.
Some power supplies come with a manual switch between something in the 110V range and something in the 220V range; here is a photo of that switch in a Lexmark printer:
This switch may be visible on the back of the desktop, but you might have to open up the case to find it.
Not all power supplies have such a switch. In some cases, it is because it automatically detects the current and adjusts accordingly— but in other cases, it is because it is designed to work only in one market, with a set voltage. You will need to find the label for the power supply unit, which should indicate what inputs it is rated for.
The above label is from a unit which only indicates compatbility with 200–240V A/C at 50–60 Hz frequencies. It would not work in the U.S., where most households are wired for 110V.
In contrast, the below label indicates the power supply unit is rated for either 115V or 230V inputs:
If your power supply not labeled that it will accept 100/110/115/120V current, or if there is no label at all, you will need to purchase a transformer.