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I am self studying and trying questions of quantitative aptitude in my mathematics exam and I am unable to solve this problem.

logic problem transcript below

Of three persons $A$, $B$ and $C$, one always lies while the others always speak the truth. $C$ asked $A$, "Do you always speak the truth, yes or no?" He said something that $C$ could not hear. So, $C$ asked $B$. "what did $A$ say?" $B$ replied, "$A$ said No".

So, who is the liar?

The answer, supposedly, is

$B$.

Unfortunately, I am completely clueless on how to approach this question. Any help would be really appreciated!

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  • $\begingroup$ It would help if you gave the question to which “B” is the answer. I assume the question is “Who always lies?” $\endgroup$ – Damila Jun 21 at 5:04
  • $\begingroup$ @Damila I am really sorry. I cropped by mistake the last line" So, who is the liar" ? Kindly accept apologies!! $\endgroup$ – user795826 Jun 21 at 5:10
  • $\begingroup$ It’s ok! If you don’t mind, I hid the answer in your question for future readers. $\endgroup$ – Damila Jun 21 at 5:16
  • $\begingroup$ @Damila since I cannot see your edit suggestion, I added the spoiler tag myself. (at)user795826 can you please provide the source of this problem? The title of the book from which this puzzle came from should be enough $\endgroup$ – melfnt Jun 21 at 8:58
  • $\begingroup$ @melfnt its from previous year papers of an exam. Not from a book. $\endgroup$ – user795826 Jun 22 at 7:45
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If the question posed is "Who always lies?" then the answer is indeed.

$B$.

We can approach this problem by noticing that

$A$ must have said "yes," yet $B$ claimed that $A$ said "no."

This can be deduced like this:

$A$ is asked "Do you speak the truth?"

- If $A$ is truthful, they will truthfully say "yes."
- If $A$ always lies, they will lie and say "yes."

Therefore, $A$'s answer to the first question is always "yes." Hence, by claiming that $A$ said "no," $B$ is the liar.

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