Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?
Answer & explanation
Answer: (d) 5/6
Each fraction has the form n/(n + 1). Adding 5 to both parts changes it by 5/[(n + 1)(n + 6)], which shrinks as n grows. So 5/6, the largest, changes least (by 5/66).
- 2/3 → 7/8: change 7/8 − 2/3 = 5/24 ≈ 0·208.
- 3/4 → 8/9: change 5/36 ≈ 0·139.
- 4/5 → 9/10: change 5/50 = 0·1.
- 5/6 → 10/11: change 5/66 ≈ 0·076 — the smallest.
Remember · Adding the same number to top and bottom pushes a proper fraction towards 1; fractions already closer to 1 move less.
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). ·