UPSC CAPF AC 2025 Paper 1 · Question 56

Question 56 of the UPSC CAPF (AC) 2025 Paper I (3 August 2025). Try it first, then open the answer and explanation.

1. CAPF 2025 · P-I · Q56 · General Mental Ability · Numbers & Series

   For any three natural numbers a, b and c, if (bc + 1)/(abc + a + c) = 11/43, then the value of abc is

   1. 30
   2. 45
   3. 60
   4. 75

   किन्हीं तीन धनपूर्णांक (natural numbers) a, b और c के लिए यदि (bc + 1)/(abc + a + c) = 11/43, तो abc का मान है

   1. 30
   2. 45
   3. 60
   4. 75
   Show answer

   Answer: (1) 30

   उत्तर: (1) 30

   Invert: (abc + a + c)/(bc + 1) = a + c/(bc + 1) = 43/11 = 3 + 10/11, and since c/(bc + 1) < 1, a = 3 and c/(bc + 1) = 10/11. Inverting again, b + 1/c = 11/10 = 1 + 1/10, so b = 1 and c = 10, giving abc = 3 × 1 × 10 = 30.

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