The correct answer is: Only assumption I is implicit.
Sachin’s mother instructed him to return home by train if it rains heavily. This means that Sachin’s mother believes that it is possible that it will rain heavily, and that if it does rain heavily, it is important for Sachin to return home by train.
Assumption I is that Sachin may not be able to decide himself if it rains heavily. This is a reasonable assumption, as Sachin may not have access to weather forecasts or may not be able to judge the weather conditions accurately.
Assumption II is that the trains may ply even if it rains heavily. This is not a necessary assumption, as the trains may be cancelled or delayed in bad weather.
Therefore, only assumption I is implicit in the statement.