Electronic voting machines usually calculate the results through a computer program. A computer program is almost always going to be faster than any other method of tabulating votes. So, yes Electronic Voting Machines provide more rapid results than other types of voting systems. They are especially faster than hand counting votes.
Electronic voting machines provide more rapid results than other types of voting systems because they limit questions regarding voter intentions. In paper systems, there is much debate about questionable markings and hanging chads. Much of the determination is left to those counting the votes, which slows the counting process. Electronic machines are more definitive, which allows for votes to be counted faster.