In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and choose the appropriate answer.

Among five boxes — P, Q, R, S, and T — each having a different weight, which one is the heaviest?

Statements:

(I) R is heavier than Q but lighter than T. P is lighter than only one box.

(II) P is heavier than Q and T, but lighter than S. T is heavier than R but lighter than S.

Statement I: R is heavier than Q but lighter than T. P is lighter than only one box.

$T > R > Q$

"P is lighter than only one box" means P is at the 2nd position from the top.

$(\text{1st Box}) > P > (\text{Remaining 3 boxes})$

Combining: We know $T > R > Q$.

• Case 1: T could be the heaviest (1st). Then the order could be $T > P > R > Q > S$.
  • Case 2: S could be the heaviest (1st). Then the order could be $S > P > T > R > Q$.

Conclusion for I: The heaviest box could be either T or S.

$\therefore$ Statement I alone is NOT sufficient.

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Statement II: P is heavier than Q and T, but lighter than S. T is heavier than R but lighter than S.

1. Inequalities:
   • "P is heavier than Q and T": $P > Q$ and $P > T$.
   • "P is lighter than S": $S > P$.
   • Combining these: $S > P > T$ and $S > P > Q$.
2. Adding R:
   • "T is heavier than R": $T > R$.
3. Final Chain:

Combining all data:

• $S > P > T > R$
  • $S > P > Q$

Conclusion for II:

In all relationships, S is heavier than P, and P is heavier than T, R, and Q. Therefore, S is the heaviest box.

$\therefore$ Statement II alone is sufficient.

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Data in Statement I is insufficient, but data in Statement II provides a unique answer.