एक 2-अंकों वाली संख्या तथा इन अंकों के स्थानों को परस्पर बदल कर प्राप्त होने वाली संख्या का अंतर 54 है ।
निम्नलिखित कथनों पर विचार कीजिए :
- 1.इस संख्या के दोनों अंकों का योगफल केवल तभी निकाला जा सकता है जब दोनों अंकों का गुणनफल ज्ञात हो ।
- 2.इस संख्या के दोनों अंकों के बीच के अंतर को निकाला जा सकता है ।
उपर्युक्त कथनों में से कौन-सा/कौन-से सही है/हैं ?
Read this question in English
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.
Consider the following statements:
1. The sum of the two digits of the number can be determined only if the product of the two digits is known.
2. The difference between the two digits of the number can be determined.
Which of the above statements is/are correct?
(a) 1 only · (b) 2 only · (c) Both 1 and 2 · (d) Neither 1 nor 2
उत्तर और व्याख्या · explanation in English
Answer: (b) केवल 2
A 2-digit number and its reverse differ by 9 times the difference of the digits, so 54 means the digits differ by 6 — that is fixed. The digit sum could be 6, 8, 10 or 12; a known product would settle it, but so would other information, so 'only if the product is known' is not true.
- (10a + b) − (10b + a) = 9(a − b), so 9 × (difference of digits) = 54.
- The digits differ by 6 — Statement 2 is correct.
- Possible numbers: 60, 71, 82, 93 (or 17, 28, 39 the other way round), with digit sums 6, 8, 10, 12.
- Knowing the product (0, 7, 16 or 27) would fix the sum, but so would other clues, such as the larger digit — the product is not the only way, so Statement 1 is incorrect.
- ✗ 1. The product is one way to fix the sum, not the only way, so 'only if' makes the statement false.
- ✓ 2. 9 × (difference of digits) = 54 gives a difference of 6.
Remember · Number − its reverse = 9 × (difference of digits); number + its reverse = 11 × (sum of digits).
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). ·