"Well sir", said Birbal turning to the first man," I think you always tell the truth. Tell me, then, if I asked this lying friend of yours which of these paths I should take, what would he say?"
"Why, this one sir", said the man. And Birbal took the OTHER path, and reached Ardhasatya safely.
How? Well, it is clear that one of the men is a liar, and one a truthteller. Suppose the first man was the truth teller; Then if Birbal asked the second man (the liar) to show the right path, he would point to the WRONG path. The first man would truthfully report this by pointing out the wrong path too; so all that Birbal had to do is to take the other path.
But what if the second man was the truth teller? Well, then he would point out the right path, but the first man would lie about it, and point out the wrong path! So Birbal's course is the same: Take the other path!.