Step 1: Understanding the Question.
Sentence i, "On the basis of experiments with rats", is fixed as the opener, and sentence vi, "and be vigorous in their eighties and nineties.", is fixed as the close. We arrange ii, iii, iv and v in between.
Step 2: Key Approach.
The paragraph is a conditional statement reported by someone. Reported speech needs a reporting clause, and a conditional needs an "if" clause followed by a result clause. Find those three pieces and the order writes itself.
Step 3: Fitting the pieces.
Sentence i is only an introductory phrase, so it must be followed by the main clause that says who is speaking. Sentence ii, "health experts here say that", is exactly that reporting clause, so ii comes first among the middle sentences.
The word "that" at the end of ii opens a reported clause, and sentence v, "if humans eat less,", starts that clause with the condition. So ii is followed by v.
The condition is a list of three things humans must do: eat less, exercise more and consume vitamins. Sentence iii, "exercise more and consume vitamins,", carries the second and third items, so iii follows v.
Only the result clause is left. Sentence iv, "they will live up to 100 years or more", is the consequence, so iv comes last among the middle sentences, and vi extends it with "and be vigorous in their eighties and nineties."
Step 4: Reading the full paragraph.
i, ii, v, iii, iv, vi gives: "On the basis of experiments with rats, health experts here say that if humans eat less, exercise more and consume vitamins, they will live up to 100 years or more and be vigorous in their eighties and nineties." The middle order is ii, v, iii, iv.
Step 5: Why the other options fail.
Option (A) ii, iii, v, iv breaks the list: it reads "say that exercise more and consume vitamins, if humans eat less", which has no subject for "exercise".
Option (C) ii, v, iv, iii puts the result before the rest of the condition, giving "if humans eat less, they will live up to 100 years or more, exercise more and consume vitamins", so the actions become results instead of conditions.
Option (D) v, ii, iii, iv puts the "if" clause before the reporting clause, so "On the basis of experiments with rats, if humans eat less, health experts here say that..." leaves the opening phrase attached to nothing sensible.
Final Answer:
The correct sequence of the middle sentences is ii, v, iii, iv, which is option (B).