Question

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 is 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 ilterate.
3. A quarter of the villagers who have their own houses cultivate paddy.
4. Half of the villagers who cultivate paddy are literate.

Answer 1

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

Let the total number of Villagers be 120

Half of the villagers of a certain village have their own houses.

So, the number of Villagers who have their own houses = 1/2 × 120 = 60

One-fifth of the villagers cultivate paddy.

The number of villagers who cultivate paddy = 1/5 × 120 = 24

One-third of the villagers are literate.

The number of villagers who are literate = 1/3 × 120 = 40

and, the number of villagers who are below 25 = 4/5 × 120 = 96

Given statements are:

1) All the villagers who have their own houses are literate. → All the villagers who have their own house are 60 and those who are literate are only 40 so this statement can't be true.

2) Some villagers under twenty-five are literate. → As the number of villagers under twenty-five are 96 and the number of literates is 40. 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, the correct answer is "Option 2".