UPSC Prelims 2010·GS1·polity-and-governance·social justice and international relations

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?

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Last updated 8 Jul 2026, 4:39 pm IST
  1. AAll the villagers who have their own houses are literate
  2. BSome villagers under twenty five are literateCorrect
  3. CA quarter of the villagers who have their own houses cultivate paddy
  4. DHalf of the villagers who cultivate paddy are literate

Explanation

To determine which statement is certainly true, we look at the overlap between the different groups of villagers.

The total population of the village is represented as 100 percent. According to the question, 1/3 of the villagers are literate, which is approximately 33.33 percent. Meanwhile, 4/5 of the villagers are below twenty-five years of age, which is 80 percent.

If we add these two groups together, 33.33 percent plus 80 percent equals 113.33 percent. Since the total population cannot exceed 100 percent, there must be an overlap of at least 13.33 percent. This means that at least some villagers must fall into both categories: they are both literate and under twenty-five.

Therefore, Option B is certainly true because it is mathematically impossible for these two groups to be entirely separate. Options A, C, and D cannot be proven as certainly true because we do not have enough specific data about how those groups overlap.

polity-and-governance: Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third
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