What would the characters know?
Simply put: The DC isn't something 'real' or substantial in the game-world. You can't say "Well, picking this lock has a difficulty of 15, and you did 12 lockpickyness. So, sorry champ'. A character doesn't know exactly how difficult it is. The same goes for their skills. A character doesn't actually know he has a strength of 17, for instance.
However, keep in mind that characters DO know what they're good at, and that certain things are more difficult than others. For instance, they might see a lock with a DC of 50. You can tell them "This lock looks VERY difficult to pick." If they roll, say, a total of 48, you don't have to say "Nope, you failed". You can also describe it as "You can hear the lock's mechanism giving way. You're getting closer, when suddenly, at the last moment, you get stuck." Again, the same goes for skills. A character may not know that their charisma is +2 and someone else's is +5, but they MAY say that "Damn, that guy is, like, twice as charismatic as I am!"
TLDR: DC's are hidden because player-characters don't know DC's in-game. They can't technically use math to determine exactly how difficult one task is opposed to another task. They CAN, however, make well-educated assumptions. As such, you should give a more elaborate description than just 'yes' or 'no'. Instead, go with 'You got close' or 'you failed miserably' or even 'You coulda done this with your eyes closed'.