यदि भिन्नों 2/3, 3/4, 4/5 और 5/6 के अंश और हर दोनों में 5 जोड़ दिया जाता है, तो निम्नलिखित में से किस एक के मान में न्यूनतम परिवर्तन होगा?
Read this question in English
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?
(a) 2/3 · (b) 3/4 · (c) 4/5 · (d) 5/6
उत्तर और व्याख्या · explanation in English
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). ·