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 ?

(a) All the villagers who have their own houses are literate.
(b) Some villagers under 25 years of age are literate. ✓ UPSC's answer
(c) Only half of the villagers who cultivate paddy are literate.
(d) No villager under 25 years of age has his own house.

Why the answer is (b)

• Let the total number of villagers be 100 for ease of calculation.

• The number of villagers under 25 years of age is 4/5 of 100, which equals 80.

• The number of literate villagers is 1/3 of 100, which is approximately 33.33.

• The sum of the number of villagers under 25 (80) and the number of literate villagers (33.33) is 113.33.

• Since the total population is only 100, the sum of these two groups exceeds the total population, meaning there must be an overlap between the two sets.

• Therefore, it is certainly correct that some villagers under 25 years of age are literate.

Why the other options are wrong

(a) All the villagers who have their own houses are literate.: The problem does not provide information linking house ownership to literacy, so it is not certain that all house owners are literate.
(c) Only half of the villagers who cultivate paddy are literate.: There is no data connecting paddy cultivation to literacy rates, making this statement unverifiable and not certainly correct.
(d) No villager under 25 years of age has his own house.: The overlap calculation proves that some villagers under 25 must be literate, but it does not prove that no villager under 25 has a house; in fact, the sets could overlap in various ways.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.