One of four suspects A, B, C and D has committed a crime. A and D are always truthful, and B and C are always untruthful. C and D are identical twins and the interrogator does not know who is who. If A says, "D is innocent", B says, "A is guilty" and among C and D one says, "A is innocent" and the other says, "B is guilty", then which of the following is FALSE?
This problem involves analyzing statements made by suspects with known truth-telling or lying tendencies to determine their guilt or innocence and identify which statement is false. We have four suspects: A, B, C, and D. A and D always tell the truth, while B and C always lie. C and D are identical twins, making it tricky to distinguish them initially.
Suspect Analysis and Statement Evaluation
Let's break down the information given:
- A: Truthful
- B: Untruthful (Liar)
- C: Untruthful (Liar)
- D: Truthful
C and D are twins, one truthful (D), one untruthful (C).
Evaluating Individual Statements
- A says, "D is innocent": Since A is always truthful, this statement is true. Therefore, D is innocent.
- B says, "A is guilty": Since B is always untruthful, this statement is false. The opposite must be true. Therefore, A is not guilty (A is innocent). This aligns with A being truthful, as a truthful person is unlikely to be the criminal.
- Among C and D, one says, "A is innocent" and the other says, "B is guilty":
- We know D is truthful and C is untruthful.
- We know "A is innocent" is a true statement (from evaluating A's and B's statements).
- Since D is truthful, D must be the one who says the true statement. Thus, D says, "A is innocent".
- This leaves C, the untruthful twin, to say the other statement: C says, "B is guilty".
- Since C is untruthful, C's statement "B is guilty" must be false. The opposite is true: B is not guilty (B is innocent).
Summary of Deductions
Based on the statements and the nature of the suspects, we can deduce the following:
- A is truthful and innocent.
- B is untruthful and innocent.
- D is truthful and innocent.
- C is untruthful. C said "B is guilty" which is a lie. If B is innocent (which we deduced), then C lied. This fits C's nature. Since only one suspect committed the crime, and A, B, and D are innocent, C must be the guilty one.
Let's summarise who is truthful/untruthful, who is innocent/guilty, and what each person said:
| Suspect | Truthful/Untruthful | Innocent/Guilty | Statement Made | Truth of Statement |
|---|---|---|---|---|
| A | Truthful | Innocent | "D is innocent" | True |
| B | Untruthful | Innocent | "A is guilty" | False |
| C (Twin) | Untruthful | Guilty | "B is guilty" | False |
| D (Twin) | Truthful | Innocent | "A is innocent" | True |
Evaluating the Options
We need to find the statement among the options that is FALSE based on our deductions.
- D said "A is innocent": From our analysis, D (the truthful twin) said "A is innocent". This statement is TRUE.
- D is innocent: From A's statement and our deductions, D is indeed innocent. This statement is TRUE.
- B is innocent: From C's lie ("B is guilty"), we deduced that B is innocent. This statement is TRUE.
- C is innocent: From our deductions, C is the untruthful twin who lied about B, and is the only remaining suspect who could have committed the crime. C is guilty, not innocent. This statement is FALSE.
Therefore, the statement that is FALSE is "C is innocent".
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
