Thanks Dan!!! great overall response!! Ill buy this one then, Ill check before the stainless steel as well. 
Take care!

That style should work provided the pipe between your resonator, which you want to keep, and your muffler, which you want to replace, is in good condition and you can cut it so that you have enough pipe left to fully join the new muffler (silencer) inlet pipe to it.
The one you pictured has a swaged inlet pipe end (increased diameter to fit over a standard pipe, so it should fit - IF the pipe you cut is the right diameter.

Bear in mind also that exhaust systems rust from the inside out. A pipe can look good from the outside and even "ring" when tapped with a wrench or small hammer, but be ready to rust through from the inside. I knew a mechanic who tested pipe condition with a pair of channel-lock pliers. If he could squeeze with one hand and deform the pipe, it was too rusty to work with.

I would recommend Stainless, otherwise you will be replacing the exhaust more often.

Dan,
This set attached is the one I am seeing for my vehicle, I guess I will use same silencer already in my vehicle?? so do you think this will fit??? it says RC40-10
I am ok with some noise since I wont use it as a daily driver so noise adds more fun which I still think that wont be that bad since it will have the silencer, correct?  

Hi Leo,

I have a stainless steel RC40, side exit with the tapered tailpipe. My particular version does not have the resonator, but produces a really nice idle and part-throttle sound. It is a little noisy at speed, though a Mini has so many noises coming in it is sometimes hard to tell which noise is which. In hind-sight I'd probably go for the version with the resonator (it was a budget issue at the time). I'd also go with the straight tailpipe.
Some say stainless steel systems are noisier because the metal is harder and more resonant -  exhaust sound goes through it. This is also an issue with SS exhaust headers, apparently. I have no way to compare, but I'm very happy with my setup.

Dan,
Thanks for your full reply & the time to respond.
My vehicle is a 1993 Mini (Rover) with the 1.3 litter Engine (1275) and I bought it with an aftermarket exhaust that goes in the middle and overall the vehicle is in pristine condition and the only thing I want to change is the muffler and end pipe to make it look as it was originally. I saw the RC 40 (S TYPE) here at the MimiMania site so seems like the regular RC 40 and the S TYPE are very similar except for the tail pipe that looks a little more thicker in the pipe of the tail pipe. So I don't know if this will fit, looks like my vehicle has the original resonator right in the middle of the vehicle and they attached the silencer and the center large exit. So I would like to buy the S type side exit muffler but do you know if this will add also a sporty sound to the car? Looks like the silencer will do the job to minimize sound....
Again thanks for your quick & very useful reply my friend!!????

Leo

Mini exhaust systems come in all shapes and sizes.The size relates more to the displacement and state of tune of the engine. A standard 850 or 998 cc engine does not need a large bore (e.g. 2") exhaust system and would not work optimally with it. A 1275 mildly upgraded would work well with a 1.75" RC40 system.

I mention size because the "muffler" you refer to must match the diameter of your existing exhaust system, starting at the engine. If your car has a stock, cast iron manifold, they are usually connected to a down pipe that might be in the 1.25" to 1.5" range (maybe smaller?).
If your car has been upgraded to a separate intake manifold and an exhaust header, then you need to measure the output end of the header.

Look at the attached image:
From the header or down-pipe, the long. slightly kinked pipe in the attached picture leads back to the muffler section. (it is kinked to work its way around the floor mounted shifter and hand-brake.)

In the picture, the "muffler" consists of two sections (often referred to as a twin-box setup) - the smaller one is a resonator and the large one is the "silencer". They work together to reduce the exhaust sound. This is what is referred to a "side-exit" setup: the tailpipe comes out the back of the car near the left side. "Centre exit" would come out below the middle of the bumper.

To complicate matters, early Minis did not originally have a resonator, just the silencer. To add to that confusion, later Minis also had a catalytic converter.

Tailpipes: this is another variation. The simplest is a straight pipe that does not increase in diameter. It probably works best. The next is the tapered variety, where the silencer end might be 1.75" and the outer end might be 2.25"and have a pretty rolled rim on it.

You will also see mention of a "RC40" exhaust system. This is a system specifically designed for the Mini A-series or A+ series engine. It is tuned in length and diameter to provide the optimum format which actually helps the engine flow better.

You need to get under your car and find out what you have now. Buy something that fits properly from beginning to end. Adapters usually just add places for leakage.

Depending on where you live and how much an impact shipping charges might be, consider a stainless steel system so you won't need to be replacing it every few years. Mild steel ones eventually rust out.

My preference: stainless steel RC40 system, side exit, straight tailpipe.

Hello,
Want to change an aftermarket muffler to an orginal side Muffler to my Classic Mini. Is the S type sold here in Mini Mania a good fit and does it adds better sound to the vehicle? I see they sell a couple mufflers with end pipes look similar but the difference between the S type and the regular in price is significant although both options are affordable for me... what do you recommend?
Thanks!