My S50 backfires when I close the trottle.

If what you are saying is that when you reach maximum rpm the car backfires, first be aware that most ignition modules have two sections--one for low rpm and one for high rpm. Could be bad ignition module. Also possible that some tune up item (plug wires, dist. cap) is bad, or that the engine is running too lean at high rpms (bad fuel pump, dirty filter, etc.)

one of the cylinders is missing. It doesn't fire sometimes and when it does, you get the backfire. Check the plugs. It should be obvious which cylinder is at fault.

There are two kinds of backfires, one is produced from the engine air intake and the other is produced from the tail pipe of the exhaust system. The cause for a backfire condition can vary depending on the malfunction of a particular system. Some backfires can be extreme enough to cause damage to related components. Anytime a backfire is observed immediately diagnose and repair as needed. If the engine is running rough it can produce a backfire. A backfire occurs when there is an imbalance in the air to fuel ratio required for your vehicle to operate properly. If the fuel mixture is too lean (not enough fuel) you may have a backfire in the intake manifold gasket, or too rich (too much fuel) you may get a backfire out of the exhaust system. It is important to observe the location of the backfire.

sounds like the catalydic converter is plugged/partial blocked- replace

Backfire is usually a timing issue so if it isn't happening at idle and the timing is correct at idle when set according to spec then the problem is the vacuum advance not functioning correctly.

You should change spark plugs. If you you have after market pipes you need to have it rejeted or the problem will continue.

it sounds like a air lock in the cooling system wen themostat opens its ok
try bleeding the cooling system

If there are aftermarket exhaust pipes on your bike, the carburetor should have been rejetted at the same time. It does sound like a lean issue, especially where your spark plugs are tan/white. It's not going to hurt anything to be a little lean, just have an annoying backfire. The only time you should have to worry is if your plugs have no color but white and it backfires while riding, not only downshifting. If you are concerned about the backfiring, I would suggest changing jets, especially the pilot jet. The pilot jet is where you are getting your backfire from. When you let off the throttle and downshift, the main jet circuit is closed and fuel is pulled through the pilot circuit. The pilot circuit cannot provide as much fuel as the main circuit, especially when the motor pulls higher rpms on downshift. This will cause a lean backfire. I know it has been several months since you posted this and you may have this corrected already, but I just stumbled upon your question. Hope this helps, Daniel.

2 things need to be done first start your bike get a can of wd40 after your bike is warm and running spray around the carb jointsall 4 of them if your engine changes rpms up or down you have a intake leak ether your carb joint gaskets or o-rings need replacing or your carb joints are old and need replacing. at this point wont hurt to have you carbs cleaned also

check ur plug wires they might be mismatched ...joe