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There is a lot of interest in the first five ranks 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. Dev roop a stood first E. Esha got the fourth position
The Answer will be A.
With the first information, we can say that none of them have positions as A, B, C, D, E ( Representing persons with their initials)
Now with the second information, guessed order was D, A, E, C, B where 2 positions are correct and 2 people with their predecessors were right.
So possible pairs of predecessors will be (CB), (EC), (AE) , (DA) now considering different cases of predecessors to be true and confirming the order with the information as 2 positions were right in second guess and none of the people have their positions mentioned in first guess we will get order of ranking as EDACB. Hence answer will be A.
Solution:
It is given that A - 1, B - 2, C - 3,D - 4 and E - 5 is wrong.
The rank of none of the student matched and no student followed her immediate predecessor.
D - 1, A - 2, E - 3, C - G, B - 5 has two correct and two students correctly followed the predecessor.
The two conditions can be satisfied when either 1 and 2 or 4 and 5 are correct rankers and one of these two pairs is the one which correctly followed the predecessor. The other one which correctly followed the predecessor should be one from the other three.
Case (i):
D - 1, A - 2 are correct ranks. In this case, C - 4 or B - 5 correctly followed the predecessor apart from A - 2. Then the possible correct arrangements are:
Case (a):
D-1
A-2
B-3
E-4
C-5
Case (b):
D-1
A-2
C-3
B-4
E-5
Here in (b) C - 3 and E - 5 are same as the guess made by the first student in which all are wrong. Hence, (b) is eliminated.
In case (a) B is following A as in the guess made by the first student. Hence (a) is also eliminated.
case (ii):
C - 4, B - 5 are correct ranks.
Now, A could not have gotten rank 1 or 2 (since the guesses made by the students regarding A's position is wrong).
A should have gotten the third rank.
D could not have secured the first rank. Therefore, E should have secured the first rank and D should have secured the second rank.
Hence, it is true that Ankit got the third position.
Choice (A)
