S1 : Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.

S2 : Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.

Question: Which one of the following statements is correct?

The correct option is: ‘Whose weight is greatest’ cannot be determined.

Let us analyze the given statements mathematically to see why the greatest weight cannot be uniquely determined. Let the weights of Sohan, Mohan, and Rohan be represented by $S$, $M$, and $R$ respectively. All weights are positive quantities (greater than zero).

From statement S1, we are given that twice the weight of Sohan is less than the weight of Mohan or that of Rohan. This gives us two inequalities:
1) $2S<M$
2) $2S<R$
Since $S>0$, these inequalities imply that $S<2S<M$ and $S<2S<R$. Thus, Sohan's weight is strictly less than both Mohan's and Rohan's weights ($S<M$ and $S<R$). This rules out Sohan from having the greatest weight.

From statement S2, we are given that twice the weight of Rohan is greater than the weight of Mohan or that of Sohan. This gives us:
3) $2R>M$
4) $2R>S$
Note that inequality (4) is already consistent with and weaker than what we know, since $R>2S>S$, which easily satisfies $2R>S$.

Now we evaluate who has the greater weight between Mohan ($M$) and Rohan ($R$). Let us check if both cases are possible:
- Case A: Suppose $S=10$, $R=25$, and $M=30$.
Here, S1 is satisfied because $2S=20$, which is less than both $M=30$ and $R=25$.
S2 is satisfied because $2R=50$, which is greater than both $M=30$ and $S=10$.
In this case, Mohan is the heaviest ($M>R>S$).

- Case B: Suppose $S=10$, $R=30$, and $M=25$.
Here, S1 is satisfied because $2S=20$, which is less than both $M=25$ and $R=30$.
S2 is satisfied because $2R=60$, which is greater than both $M=25$ and $S=10$.
In this case, Rohan is the heaviest ($R>M>S$).

Since both scenarios are mathematically valid and satisfy all the conditions given in S1 and S2, we cannot uniquely determine whether Mohan or Rohan has the greatest weight. Therefore, ‘Whose weight is greatest’ cannot be determined.