Question

Three teachers P.Q, R were talking about six students A, B, C, D, E and F who wrote an examination in Physics.
P predicted that B, D, A and C would get 1st, 2nd, 3rd and 4th ranks respectively and the other two would fail.
Q predicted that E.B.A and Fwould get 1st, 2nd, 3rd and 4th ranks respectively and the other two would fail.
R predicted that A, D, Fand E would get 1st 2nd, 3rd and 4th ranks respectively and the other two would fail.
When the results were announced, it was found out that: Exactly two persons got the same ranks as predicted by P, one student got the same rank as predicted
by Q and one student got the same rank as predicted by R. Exactly two students who were predicted to pass by P, failed Exactly, one student who was
predicted to pass by Q, failed. Exactly one student, who was predicted to pass by R. failed.
Who is the 3rd ranker?
​

Answer 1

Answer

E is the third ranker

Explanation

→ According to P

B - 1st

D - 2nd

A - 3rd

C - 4th

E and F - fail

→ According to Q

E - 1st

B - 2nd

A - 3rd

F - 4th

C and D- fail

→ According to R

A - 1st

D - 2nd

F - 3rd

E - 4th

B and C - fail

Now,

• Exactly two persons got the same rank as predicted by P
• One student got the same rank as predicted by Q
• One student got the same rank as predicted by R
• Exactly two students predicted to be passed by P, failed
• Exactly one student predicted to be passed by Q, failed
• Exactly one student predicted to be passed by R, failed

Let B and D get the 1st and 2nd rank. Then, exactly two persons got the same rank as predicted by P

Now, as per Q, only F can get 4th rank because if E and B would get 1st and 2nd, it would contradict P and if A gets third, then three person would get the same rank as predicted by P

For R, only D can get 2nd rank now.

Since B and D have passed, as per P, A and C would have to fail

⇒ As predicted by Q, A as third, A would fail

⇒ As predicted by R, A as first, A would fail

So, we get

• Exactly two persons got the same rank as predicted by P = B (1st) and D (2nd)
• One student got the same rank as predicted by Q = F (4th)
• One student got the same rank as predicted by R = D (2nd)
• Exactly two students predicted to be passed by P, failed = A and C
• Exactly one student predicted to be passed by Q, failed = A
• Exactly one student predicted to be passed by R, failed = A

So, we get none of them is contradicted, so we can conclude

B is 1st

D is 2nd

F is 4th

A and C have failed

So, only E is left, hence E is the third ranker.