एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।
P और Q में से प्रत्येक की आयु 100 वर्ष से कम है किन्तु 10 वर्ष से अधिक है। यदि आप P की आयु के अंकों का विनिमय (इंटरचेंज) कर दें, तो यह संख्या Q की आयु को निरूपित करती है।
- प्रश्न: उनकी आयु में कितना अंतर है?
- कथन–I: P की आयु, Q की आयु से अधिक है।
- कथन–II: उनकी आयु का योगफल, उनकी आयु के अंतर का 11/6 गुना है।
उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?
Read this question in English
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.
Question. What is the difference of their ages?
Statement–I. The age of P is greater than the age of Q.
Statement–II. The sum of their ages is 11/6 times their difference.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together
उत्तर और व्याख्या · explanation in English
Answer: (a) प्रश्न का उत्तर, दोनों में से अकेले एक कथन का प्रयोग कर दिया जा सकता है, किन्तु अकेले अन्य कथन का प्रयोग कर नहीं दिया जा सकता है
With ages 10a + b and 10b + a, Statement II gives 11(a + b) = (11/6) × 9|a − b|, i.e. 2(a + b) = 3|a − b|, whose only solution is 51 and 15. The difference is 36 whichever is older, so Statement II alone suffices; Statement I alone does not.
- Let the ages be 10a + b and 10b + a, with a and b non-zero digits. Sum = 11(a + b); difference = 9|a − b|.
- Statement I alone only says which one is older, so it is not sufficient.
- Statement II: 11(a + b) = (11/6) × 9|a − b|, which simplifies to 2(a + b) = 3|a − b|.
- If a > b: 2a + 2b = 3a − 3b, so a = 5b; b = 1 gives a = 5 (b = 2 would need a = 10). The ages are 51 and 15, in some order.
- Difference = 36 either way, so Statement II alone answers the question.
- Check: 51 + 15 = 66 = (11/6) × 36.
Remember · For a number and its reverse: sum = 11(a + b), difference = 9(a − b). Ask only what the question actually needs.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·