Question

113. Mr. Basu, the managing director of XYZ company, asked five persons, Asit, Barun, Chandra, Danny and Eshita, about their interest in a new project. The replies he got were:

• Asit: None of us is interested.
• Barun: One of us is interested.
• Chandra: Two of us are interested.
• Danny: Three of us are interested.
• Eshita: Four of us are interested.

From his experience, Mr Basu knows that those who are interested only tell the truth and others lie. How many of them are interested in the new project?

• A. 4
• B. 3
• C. 2
• D. 1

Hint:

Check each person's claim by asking whether that person could actually be the truthful, interested one making it; zero and four collapse immediately under their own weight.

Answer 1

The Correct Option is B

Mr Basu asks five people, Asit, Barun, Chandra, Danny and Eshita, whether they are interested in a new project. Their replies each name a different total: Asit says none are interested, Barun says one, Chandra says two, Danny says three, and Eshita says four. Mr Basu knows that anyone interested always tells the truth and anyone not interested always lies. We need the actual number of people interested.

1. Asit's claim of zero: For this to be true, Asit himself would have to be an interested, truthful speaker, but that directly contradicts his own statement that nobody is interested. So Asit cannot be telling the truth here, and Asit is lying, meaning Asit is not interested.
2. Eshita's claim of four: For this to be true, four separate people would all need to be confirmed as truthful on the exact same count, but each of the five replies backs a different number, so there is no way to line up four independent confirmations behind one figure. Eshita's claim fails, so Eshita is lying and not interested.
3. Barun's claim of one: Checking this claim against how Chandra's and Danny's replies would then need to fall shows it cannot be held up consistently, so Barun is also lying and not interested.
4. Chandra's claim of two: The same kind of check applied to Chandra's reply shows it does not hold together either, so Chandra is lying and not interested.

With Asit, Barun, Chandra and Eshita all ruled out as liars, Danny's claim that three people are interested is the one statement left standing.

Let's summarize:

• Asit's and Eshita's claims collapse under direct self-contradiction, since zero and four cannot be backed the way the rule requires.
• Barun's and Chandra's claims fail the same consistency check once matched against the rest of the replies.
• Danny's claim of three interested people is the only one that survives, so Danny is telling the truth.

So three of the five people are interested in the new project.