Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct?

Let's denote the total number of villagers as 100%. Villagers with own houses = 1/2 = 50% Villagers who cultivate paddy = 1/5 = 20% Villagers who are literate = 1/3 = 33.33% Villagers under 25 years of age = 4/5 = 80%

Now let's analyze each statement:

A) All the villagers who have their own houses are literate. This means 50% of the villagers (those with houses) must be literate. However, only 33.33% of the total villagers are literate. It's impossible for 50% of the villagers to be literate if only 33.33% are literate in total. So, this statement is certainly incorrect.

B) Some villagers under 25 years of age are literate. Villagers under 25 = 80%. Villagers who are literate = 33.33%. To find the minimum possible overlap between two groups, we add their percentages and subtract 100% (the total). Minimum overlap = (Percentage of Group 1 + Percentage of Group 2) - 100% Minimum overlap (Under 25 and Literate) = (80% + 33.33%) - 100% = 113.33% - 100% = 13.33%. Since the minimum overlap is 13.33% (a positive number), it means at least 13.33% of the villagers are both under 25 and literate. Therefore, "some" villagers under 25 are certainly literate. This statement is certainly correct.

C) Only half of the villagers who cultivate paddy are literate. Villagers who cultivate paddy = 20%. Villagers who are literate = 33.33%. "Only half" would mean exactly 10% of the total villagers are both paddy cultivators and literate. The number of literate paddy cultivators could range from 0% (if no paddy cultivator is literate, which is possible if 20% + 33.33% is less than 100%) to 20% (if all paddy cultivators are literate). Since the overlap can vary, stating "only half" is not certainly correct.

D) No villager under 25 years of age has his own house. Villagers under 25 = 80%. Villagers with own houses = 50%. Minimum overlap (Under 25 and Own House) = (80% + 50%) - 100% = 130% - 100% = 30%. Since the minimum overlap is 30%, it means at least 30% of the villagers are both under 25 and have their own house. Therefore, the statement that "no villager" under 25 has his own house is certainly incorrect.

The final answer is B