If liars always lie and truthful persons never, and in a group of 10 persons everyone calls all others liars, then the number of liars among the 10 is

Correct option is B

Solution:

Assumptions:

1. Liars always lie (their statements are false).
2. Truthful persons always tell the truth (their statements are true).
3. Each of the 10 persons says, "Everyone else is a liar."

Step 1: Consider the Statements

• If a truthful person says, "Everyone else is a liar," this means all 9 others are indeed liars.
• If a liar says, "Everyone else is a liar," this statement is false, meaning not everyone else is a liar (there is at least one truthful person).

Step 2: Logical Analysis

1. If there is 1 truthful person, their statement implies that all 9 others are liars. This is consistent because a truthful person always tells the truth.
• In this case, the group consists of 1 truthful person and 9 liars.
2. If there are more than 1 truthful person, their statements would contradict each other because they would claim that "everyone else is a liar," which cannot be true if there is more than 1 truthful person.
3. If there are 0 truthful persons, then everyone is a liar, and their statements would contradict the definition of a liar (their statements must be false, but "everyone else is a liar" would then be true).

Step 3: Conclusion

The only consistent scenario is when there is 1 truthful person and 9 liars in the group.

Final Answer:

(b) 9 liars.