Fastest scenario for evolving pokemon such as Magikarp (400 candies)?

The quickest way I have experience to catch Magikarp is to locate a Pokestop next to a body of water. With the combination of a Luremodule and an Incense, I have witnessed people "fishing" for Magikarp. I sat there and a Magikarp was spawning roughly every 2 minutes

There's evidence that Gyarados can be found in the wild, so if you can manage that, you don't even have to evolve your Magikarp at all. Hang out around lakes, harbours and the seaside and you might get lucky (in the meantime, you'll probably catch Magikarp anyway).

Other than that though, the only way is to catch 101 Magikarp, transfer at least 97 of them¹, and then evolve 1 of them. You don't need 400 of them, because you get 3 candies for each catch and 1 for each transfer.

Eggs could help (Magikarp can hatch from 2km eggs, and you'll get much more than 3 candies for a hatch), but given the odds of 14 different Pokemon that can hatch from a 2km egg, you'll probably find it faster to specifically focus on catching Magikarp near bodies of water. If you hatch one... bonus :)

_{¹ Thanks xehpuk for the maths help ;)}