दो अंकों की धनपूर्ण संख्या का, इसके अंकों को उत्क्रमित करने से बनी संख्या से अनुपात 4 : 7 है । ऐसे युग्मों की संख्या कितनी है ?
Read this question in English
The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs is
(a) 5 · (b) 4 · (c) 3 · (d) 2
उत्तर और व्याख्या · explanation in English
Answer: (b) 4
Writing the number as 10a + b, the ratio 4 : 7 simplifies to b = 2a. The digit a can be 1 to 4, giving 12, 24, 36 and 48 — four pairs.
- Let the number be 10a + b; reversed, it is 10b + a.
- 7(10a + b) = 4(10b + a) → 70a + 7b = 40b + 4a → 66a = 33b → b = 2a.
- b must be a digit, so a = 1, 2, 3, 4.
- Pairs: 12 & 21, 24 & 42, 36 & 63, 48 & 84 — each in the ratio 4 : 7.
- Number of pairs = 4.
Remember · Turn digit-reversal conditions into 10a + b form; the equation usually gives a simple digit relation to list.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·