In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statements:
(I) Some men are educated.
(II) Educated persons prefer small families.

Conclusion:
(I) All families are educated.
(II) Some men prefer small families.

From the given statements there is information between educated people and small families but there is no information regarding all families. So all families may or may not be educated. Hence, conclusion I do not follow the given statements.

Some men are educated and educated prefer small families. So some men prefer small families. Hence conclusion II follows the given statements.

$$\therefore\ $$Only Conclusion II follows the given statements.

Hence, the correct answer is Option B