A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows:
P: I did not steal. Q stole it.
Q: R did not steal. I did not steal.
R: I did not steal. I do not know who did it.
Who stole the mobile phone?

Correct Option (A)

The problem states that only one suspect is guilty. The guilty individual lies, while innocent individuals tell the truth.

Let us assume P is the guilty party:

• If P is guilty, P's statements must be false.
  • P's statement "I did not steal" becomes false, implying P stole the mobile phone.
  • P's statement "Q stole it" becomes false, implying Q did not steal the mobile phone.
• Now, we examine the statements of Q and R, who must be innocent and therefore truthful:
  • Q's statements:
    • "R did not steal" must be true. This is consistent with R being innocent.
    • "I did not steal" must be true. This is consistent with Q being innocent.
  • R's statements:
    • "I did not steal" must be true. This is consistent with R being innocent.
    • "I do not know who did it" must be true. This is consistent with R being innocent and unaware of P's guilt.
• All statements are consistent under the assumption that P is guilty. Therefore, P stole the mobile phone.

Incorrect Options:

Let us analyze the scenarios where Q or R are assumed guilty:

• If Q is guilty:
  • Q's statements must be false.
    • Q's statement "I did not steal" becomes false, implying Q stole the mobile phone.
    • Q's statement "R did not steal" becomes false, implying R stole the mobile phone.
  • This scenario leads to a contradiction, as both Q and R would be guilty, which violates the problem's condition that only one person is guilty. Therefore, Q cannot be guilty.
• If R is guilty:
  • R's statements must be false.
    • R's statement "I did not steal" becomes false, implying R stole the mobile phone.
  • Now, we examine Q's statements, as Q must be innocent and truthful.
    • Q's statement "R did not steal" must be true.
  • This contradicts our initial assumption that R stole the mobile phone. Therefore, R cannot be guilty.
• Cannot be concluded:
  • As demonstrated, a consistent scenario is established when P is identified as the guilty party, with all statements aligning with the given conditions. Thus, a definitive conclusion can be reached.