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?
Answer & explanation
Answer: (b) Some villagers under 25 years of age are literate.
Fractions of the same village that add up to more than 1 must overlap. Under-25s (4/5) and literates (1/3) together make 17/15, so at least 2/15 of the villagers are both — some under-25s are certainly literate.
- Under 25: 4/5 of the villagers; literate: 1/3.
- 4/5 + 1/3 = 12/15 + 5/15 = 17/15, which is more than the whole village.
- So at least 17/15 − 1 = 2/15 of the villagers are both under 25 and literate — (b) is certain.
- Check the rest: house-owners (1/2) outnumber literates (1/3), so (a) is impossible; house-owners and under-25s (1/2 + 4/5 = 13/10) must overlap, so (d) is false; (c) cannot be fixed from the data.
- ✗ (a) Half the villagers own houses but only a third are literate, so not all house-owners can be literate.
- ✓ (b) 4/5 + 1/3 exceeds 1, so at least 2/15 of the villagers are both under 25 and literate.
- ✗ (c) Nothing tells us how literacy is spread among paddy growers.
- ✗ (d) 1/2 + 4/5 = 13/10 exceeds 1, so at least 3/10 of the villagers are under 25 and own a house.
Remember · If two fractions of one group add to more than 1, the excess over 1 is the guaranteed minimum overlap.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·