Mr. Vasu, the managing director of XYZ company asked five persons – Asit, Varun, Chandra, Danny and Eshita about their interest in a new project. The replies, he got were: Asit: None of use is interested. Varun: One of use is interested Chandra: Two of us are interested Danny: Three of us are interested Eshita: Four of us are interested From his experience, Mr. Vasu Known that those who are interested only tell the truth and others lie. How many of them are interested in the new project:

This is a truth-teller and liar logic problem. Each speaker's statement is true if and only if that speaker is interested. Since the number of interested people, k, is a single fixed value, at most one count-statement can be true, so only the speaker whose claimed number matches k can be interested.

• k = 0: Asit's statement would be true, so Asit must be interested. That contradicts k = 0.
• k = 1: Varun's statement is true, so Varun alone is interested. Everyone else lies. This is consistent, so k = 1.
• k = 2, 3 or 4: Chandra, Danny or Eshita would be the only truthful speaker, so only one person is interested. That contradicts the claimed 2, 3 or 4.

So option A (4), B (3) and C (2) fail for the same reason: the speaker quoting that number would be the only truthful one, which forces the count to be 1. The core concept is self-referential consistency, which appears in reasoning and logic sections, and it also trains the disciplined case-testing needed for Mains answers on evidence.

Trap: Aspirants often check whether the number mentioned matches the speakers' claims without checking who would actually be interested under that assumption.