# 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.

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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?
1. All the villagers who have their own houses are literate
2. Some villagers under twenty five are literate
3. A quarter of the villagers who have their own houses cultivate paddy
4. Half of the villagers who cultivate paddy are literate

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Correct Answer - Option 2 : Some villagers under twenty five are literate

Let the total number of Villagers be 100x

So, the number of Villagers who have their own houses = 1/2×100x = 50x

The number of villagers who cultivate paddy. = 1/5 × 100x = 20x

The number of villagers who are literate = 1/3 × 100x = 33.33x

and, the number of villagers who are below 25 = 4/5 × 100x = 80x

Given statements are:

1) All the villagers who have their own houses are literate. → All the villagers who have their own house are 50x and those who are literate are only 33.33x so this statement can't be true.

2) Some villagers under twenty five are literate. → As, the number of villagers under twenty five are 80x and number of literate are 33.33x. So, the given statement is true.

3) A quarter of the villagers who have their own houses cultivate paddy. This may or may not be true.

4) Half of the villagers who cultivate paddy are literate. → This may or may not be true.

Hence, option 2 is the correct answer.