Correct Option (b)
Let S, M, and R represent the weights of Sohan, Mohan, and Rohan, respectively.
Statement S1 provides: "Twice the weight of Sohan is less than the weight of Mohan or that of Rohan."
This can be mathematically expressed as:
- 2S < M
- 2S < R
From the inequality 2S < M, it logically follows that S < M (since weights are positive). Similarly, from 2S < R, it follows that S < R.
These two deductions collectively establish that Sohan's weight (S) is less than Mohan's weight (M) and also less than Rohan's weight (R). Consequently, Sohan's weight is the least among the three individuals.
Statement S2, "Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan" (i.e., 2R > M and 2R > S), provides additional information but does not contradict the conclusion that Sohan's weight is the least. It is consistent with Sohan having the minimum weight.
Incorrect Options:
Option (a) Weight of Mohan is least: This is incorrect. As derived from Statement S1, 2S < M directly implies that Sohan's weight (S) is less than Mohan's weight (M).
Option (c) Weight of Rohan is least: This is incorrect. From Statement S1, 2S < R directly implies that Sohan's weight (S) is less than Rohan's weight (R).
Option (d) ‘Whose weight is least’ cannot be determined: This is incorrect. The analysis of Statement S1 definitively establishes that Sohan's weight is the least, making the determination possible.