UPSC CAPF AC 2024 Paper 1 · Question 61

Question 61 of the UPSC CAPF (AC) 2024 Paper I (4 August 2024). Try it first, then open the answer and explanation.

1. CAPF 2024 · P-I · Q61 · General Mental Ability · Arithmetic

   The sum of the ages of A and B (in years) is 22. The product of their ages two years back was 77. Which one of the following is the value of the difference of their current ages?

   1. 2
   2. 3
   3. 4
   4. 5

   A और B की आयु (वर्षों में) का योग 22 है। दो वर्ष पहले उनकी आयु का गुणनफल 77 था। निम्नलिखित में से कौन-सा, उनकी वर्तमान आयु के अंतर का मान है?

   1. 2
   2. 3
   3. 4
   4. 5
   Show answer

   Answer: (3) 4

   उत्तर: (3) 4

   Let the ages be a and b: a + b = 22 and (a - 2)(b - 2) = 77, so ab - 2(a + b) + 4 = 77, giving ab = 117. The two numbers with sum 22 and product 117 are 13 and 9 (check: two years back 11 × 7 = 77), so the difference is 13 - 9 = 4.

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