Loud radiator fan noise when turning on AC

Has anyone ever experienced this problem?

When I turn on my car AC at max power, the fan in front of the engine area starts with a very loud noise that's audible in the cabin. There are some vibrations as well.

The moment I turn of the AC, the fan noise is gone.

The only solution I found is reducing the AC power by 2 points (out of 4), then there is no noise, but not sufficient cooling!

Mechanic says fan needs to replaced which will cost ₹2500+.

Any tips on how to fix this without spending a lot?