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?
Answer & explanation
Answer: (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
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). ·