Question

There is a lot of interest in the first five ranks for Class XI students. One student guessed the rank order as Ankita, Bhagyashree, Chanchal, Devroopa and Esha. Later upon announcement of the results, it was found that not only did he get each student out off her true position, none of the students in his ranking correctly followed her immediate predecessor. Another student guessed Devroopa, Ankita, Esha, Chanchal and Bhagyashree. Even his guess was wrong. It was found that he had got two positions correct, and two students in his ranking correctly followed their immediate predecessors. Which of the following is true about the correct rank order?

• A. Ankita got the third position
• B. Bhagyashree got the fourth position.
• C. Chanchal got the second position.
• D. Devroopa stood first.
• E. Esha got the fourth position.

Hint:

In complex logic puzzles, start with the most concrete and restrictive rules. Here, the rule about "two correct positions" from the second guess provides a limited number of starting points, making it much easier to solve than trying to guess the full order.

Answer 1

The Correct Option is A

Let the five students be abbreviated as A (Ankita), B (Bhagyashree), C (Chanchal), D (Devroopa), and E (Esha). The ranks are 1, 2, 3, 4, 5. We need to determine the correct ranking by applying the given rules.
Step 1: Deconstruct the clues from both guesses.
Clues from Guess 1 (A-B-C-D-E):
Rule 1.1 (Wrong Positions): No student is in their guessed position.
Rank 1 is not A.
Rank 2 is not B.
Rank 3 is not C.
Rank 4 is not D.
Rank 5 is not E.
Rule 1.2 (Wrong Pairs): No student follows their guessed immediate predecessor.
The pairs (A, B), (B, C), (C, D), and (D, E) do not appear consecutively in the correct order.
Clues from Guess 2 (D-A-E-C-B):
Rule 2.1 (Wrong Guess): The correct order is not D-A-E-C-B.
Rule 2.2 (Two Correct Positions): Exactly two students are in the positions guessed.
Rule 2.3 (Two Correct Pairs): Exactly two of the pairs from the guess—(D, A), (A, E), (E, C), (C, B)—appear consecutively in the correct order.
Step 2: Systematically test possibilities based on the strongest clues (Rule 2.2 and 2.3).
Let's analyze the possibilities for the two correct positions from Guess 2. A logical starting point is to test the combination of C being 4th and B being 5th.
Assumption: C is 4th and B is 5th. This satisfies Rule 2.2.
This implies the correct order ends in `...C-B`. This also satisfies one part of Rule 2.3, as the pair (C, B) is correct.
From our assumption (C-4, B-5), we know the other positions from Guess 2 are wrong: D is not 1st, A is not 2nd, and E is not 3rd.
We still need one more correct pair from the remaining options: (D, A), (A, E), (E, C).
The pair cannot be (E, C) because that would place E in 3rd, which we know is incorrect.
The remaining students (D, A, E) must fill ranks 1, 2, and 3.
Step 3: Test the remaining pair possibilities.
Case A: The other correct pair is (A, E).
We must arrange D, A, E in ranks 1-3 to include the pair (A, E). The possibilities are `D-A-E` or `A-E-D`.
If the order is `D-A-E-C-B`: This is the exact order of Guess 2, which is explicitly wrong (Rule 2.1).
If the order is `A-E-D-C-B`: This violates Rule 1.1, which states that Rank 1 is not A.
Therefore, (A, E) cannot be the other correct pair.
Case B: The other correct pair is (D, A).
We must arrange D, A, E in ranks 1-3 to include the pair (D, A). The possibilities are `D-A-E` or `E-D-A`.
If the order is `D-A-E-C-B`: This is the order of Guess 2, which is wrong (Rule 2.1).
If the order is `E-D-A-C-B`: This is a potential solution. Let's verify it against all rules.
Step 4: Verify the potential solution E-D-A-C-B.
Check Guess 1 Rules:
Rule 1.1 (Wrong Positions): The order is E-1, D-2, A-3, C-4, B-5. This does not match any position from A-1, B-2, C-3, D-4, E-5. (Pass)
Rule 1.2 (Wrong Pairs): The order E-D-A-C-B does not contain any of the pairs (A, B), (B, C), (C, D), or (D, E). (Pass)
Check Guess 2 Rules:
Rule 2.1 (Wrong Guess): The order is not D-A-E-C-B. (Pass)
Rule 2.2 (Two Correct Positions): Comparing E-D-A-C-B to D-1, A-2, E-3, C-4, B-5, we find that C is correctly in 4th and B is correctly in 5th. Two positions are correct. (Pass)
Rule 2.3 (Two Correct Pairs): The correct order contains the pairs (D, A) and (C, B). It does not contain (A, E) or (E, C). Two pairs are correct. (Pass)
The order E-D-A-C-B satisfies all conditions.
Step 5: Determine the final answer.
The correct rank order is:
1st: Esha
2nd: Devroopa
3rd: Ankita
4th: Chanchal
5th: Bhagyashree
Now we check the given options:
(A) Ankita got the third position. — This is true.
(B) Bhagyashree got the fourth position. — False.
(C) Chanchal got the second position. — False.
(D) Devroopa stood first. — False.
(E) Esha got the fourth position. — False.
\[ \boxed{\text{(A)}} \]