What is the greatest length x such that 3½ m and 8¾ m are integral multiples of x?
Answer & explanation
Answer: (d) 1¾ m
The greatest length that divides both is their HCF. In quarters of a metre the lengths are 14/4 and 35/4, and HCF(14, 35) = 7, so x = 7/4 = 1¾ m.
- 3½ = 14/4 m and 8¾ = 35/4 m.
- HCF(14, 35) = 7, so the greatest common length = 7/4 m = 1¾ m.
- Check: 3½ ÷ 1¾ = 2 and 8¾ ÷ 1¾ = 5, both whole numbers.
Remember · HCF of fractions: put them over a common denominator, take the HCF of the numerators, keep the denominator.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·