Question: I'm currently a high school student trying to build an ultralight aircraft from scratch (I'm self taught and still learning from educational videos), but I don't have much savings (about RM 2.5k, which converts to roughly 587 USD), so I could only afford a small engine. 

Is it possible to achieve a certain propeller's efficient rpm by using gears while still using a small engine? Like those gearboxes found in cars to increase rpm.

Answer: 
The answer is yes and no. Can an airplane be designed to fly on very low power? Yes. The Wright 1903 flyer flew on a mere 12 hp gasoline engine. The real question is not can you fly on a lower power engine but *can a lower power engine provide a meaningful flight envelope while carrying a realistic useful load over a wide range of atmospheric conditions*.

It all depends upon your performance requirements which you need to decide upon before engine selection, but the suggestion of using a VW Beetle engine is a good one. [Rotax's line of piston engines](http://www.flyrotax.com/) have also been a good choice, especially for LSA aircraft.
Actually, you'd be gearing the engine down, not up. Propellers become very inefficient if the tips go supersonic (as well as extremely noisy). You'd want to keep the prop at around 1800-2200 rpm, depending on the size of the prop. Smaller engines typically put out peak power at much higher rpm's than that, so they have to be geared down to match the prop to the engine's power curve. 

A typical ultralight engine is the [Rotax 582](https://www.flyrotax.com/produkte/detail/rotax-582-ul.html). Designed for ultralight aircraft use, it can sustain high power output for long periods of time. That is current production, so it can be a bit expensive.

Now out of production but they can be found on the used market fairly inexpensively, is the [Rotax 503](https://en.wikipedia.org/wiki/Rotax_503). It has been a very popular ultralight engine. 

Motorcycle engines may have less than desirable reliability. Typically, they are designed for brief periods of acceleration, with long periods of cruising at low power output. If you take a stock small motorcycle engine and run it wide open for long periods of time, the cylinder head will probably overheat, blowing the gasket and leaving you with no power. When that happens, you are going to come down, regardless of whether there is a safe place to land, or not.

I have seen Rotax 503's with a gearbox for ultralight use, in the USD 1500 range. More than a small motorcycle engine, but cheaper than a funeral...