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R writes the book two persons before Q. The number of persons, who writes after Q is one more than the number of persons who writes before S. The rank of neither R nor S is 1. There will be three cases: If R‘s rank is 3, then Q’s rank is 5. S’ rank will be 2. If R‘s rank is 2, then Q’s rank is 4. S’ rank will be 3. If R‘s rank is 2, then Q’s rank is 3. S’ rank will be 4. 
T writes before P. At least two persons write between S and P. V writes after U. Rank of V is not 5. T is neither first ranked neither writes just before V. Atmost two persons write between U and T. Case 1. If P‘s rank is either 6 or 7, then T’s rank is 4. As atmost two persons write between U and T. So, U’ rank will be 1. V’s rank is either 6 or 7. Case 2. This case will get discarded as we cannot place U and T. Case 3. If P‘s rank is either 6 or 7, then T’s rank is 5. As atmost two persons write between U and T. So, U’ rank will be 2. V’s rank is either 6 or 7. This case will get discarded as T is neither first ranked neither writes just before V. 
Final arrangement as shown below: 
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