Why does 1990 MTD ranch king backfire?

If it backfires after you shut it off then it is probably running too rich. Any unburned gas the that is exhausted out and into the muffler will explode with a backfire. With a 1990 model you won't have the anti-backfire solenoid on the bottom of the carb like the newer ones have. If it backfires while it is running it might be out of time. Check the keyway between the crank and flywheel to make sure it is not partially sheared.