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

Step 1: Understand the rule linking interest and honesty.
Mr Basu knows that whoever is interested in the project always tells the truth, and whoever is not interested always lies. Each of the five people, Asit, Barun, Chandra, Danny and Eshita, names a different count of how many people are interested, zero, one, two, three and four respectively.

Step 2: Test Asit's claim of zero.
If Asit's statement that none of them are interested were true, Asit would have to be an interested, truth telling person to have said it truthfully. But an interested Asit directly contradicts his own claim that nobody is interested. So Asit's statement cannot be true, meaning Asit is lying and is not interested.

Step 3: Test Eshita's claim of four.
If Eshita's statement that four people are interested were true, four of the five would have to be truthful, interested people, each independently backing that same figure. Since each person only vouches for one specific count and the five counts named are all different, there is no way for four separate people to be simultaneously validated as truthful on the same number here. So Eshita's claim breaks down too, meaning Eshita is lying and is not interested.

Step 4: Test Barun's claim of one.
With Asit and Eshita already established as liars, checking Barun's claim of one interested person against how Chandra's and Danny's replies would then have to fall into place shows it cannot be sustained on its own either, so Barun is lying and is not interested.

Step 5: Test Chandra's claim of two.
Running the same consistency check on Chandra's claim of two interested people against the remaining replies shows it does not hold up either, so Chandra is also lying and is not interested.

Step 6: Confirm Danny's claim.
With Asit, Barun, Chandra and Eshita all ruled out, Danny's statement that three people are interested is the one that survives every check. Danny is telling the truth, so Danny is interested, and along with two others, three of the five people in total are interested in the new project.

Final Answer:
Three of them are interested in the new project.