Consider two Statements and a Question: Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the- heaviest. Statement 2: A is heavier than D, but is lighter than C. Question: Who is the heaviest among A,B,C, D and E? Which one of the following is correct in respect of the Statements and the Question?

The question asks to identify the heaviest person among A, B, C, D, and E.

Let's analyze each statement:

Statement 1: "Each of A and D is heavier than each of B, E and F, but none of them is the heaviest." From this:

1. A > B, E, F
2. D > B, E, F
3. Neither A nor D is the heaviest among all the people mentioned or implied (A, B, C, D, E, F, and potentially others). This statement tells us that B and E cannot be the heaviest because A and D are heavier than them. It also tells us that A and D cannot be the heaviest. So, from the list (A, B, C, D, E), only C remains as a potential heaviest person. However, Statement 1 does not provide any information about C's weight relative to A or D. It's possible that C is lighter than A, and some unknown person 'X' (not in the list A, B, C, D, E) is the heaviest. For example, X > A > D > C > B > E. In this scenario, Statement 1 holds true, but C is not the heaviest. Therefore, Statement 1 alone is NOT sufficient.

Statement 2: "A is heavier than D, but is lighter than C." From this:

1. A > D
2. C > A Combining these, we get: C > A > D. This statement tells us that C is heavier than A and D. However, it provides no information about B and E. It's possible that B or E could be heavier than C. For example, B > C > A > D. In this scenario, B would be the heaviest. Therefore, Statement 2 alone is NOT sufficient.

Now, let's combine both Statement 1 and Statement 2: From Statement 2: C > A > D. From Statement 1: A > B and A > E (since A is heavier than B, E, F). Combining these facts: Since C > A, and A > B, it implies C > B. Since C > A, and A > E, it implies C > E. We already know C > A and C > D from Statement 2. Therefore, by combining both statements, we can conclude that C is heavier than A, B, D, and E. The phrase "none of them is the heaviest" in Statement 1 (referring to A and D) is consistent with C being the heaviest, as C is not A or D. Thus, C is the heaviest among A, B, C, D, and E.

Both Statement 1 and Statement 2 are required to answer the question.

The final answer is $\boxed{C}$