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 below twenty five. Then, which one of the following is certainly true

Explanation

We can start by representing the information given in the problem in a table: Number of villagers Proportion of villagers Own houses ? 1/2 Cultivate paddy ? 1/5 Literate ? 1/3 Below 25 years old ? 4/5 Let`s use x to represent the total number of villagers in the village. Then we can fill in the table as follows: Number of villagers Proportion of villagers Own houses x/2 1/2 Cultivate paddy x/5 1/5 Literate x/3 1/3 Below 25 years old 4x/5 4/5 Now let`s look at the options: a) All the villagers who have their own houses are literate: This cannot be true, because we know that only 1/3 of the villagers are literate, and more than half of the villagers have their own houses. b) Some villagers under twenty five are literate: This must be true, since 1/3 of the villagers are literate, and 4/5 of the villagers are below 25 years old. c) A quarter of the villagers who have their own houses cultivate paddy: This cannot be determined with the given information. We don`t know anything about the proportion of villagers who cultivate paddy among those who own houses. d) Half of the villagers who cultivate paddy are literate: This cannot be determined with the given information. We don`t know anything about the literacy rate among those who cultivate paddy. Therefore, the correct answer is (b) Some villagers under twenty five are literate.