UPSC CAPF AC 2025 Paper 1 · Question 69

Question 69 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 · Q69 · General Mental Ability · Numbers & Series

   If a^(2x) = b^(3y) = c^(5z) and b = a²c, then which one of the following is true?

   1. 2/x + 3/y = 5/z
   2. 1/x - 3/(5z) = 1/(3y)
   3. 1/x + 1/(5z) = 1/(3y)
   4. 2/x - 5/z = 3/y

   यदि a^(2x) = b^(3y) = c^(5z) और b = a²c, तो निम्नलिखित में से कौन-सा सही है?

   1. 2/x + 3/y = 5/z
   2. 1/x - 3/(5z) = 1/(3y)
   3. 1/x + 1/(5z) = 1/(3y)
   4. 2/x - 5/z = 3/y
   Show answer

   Answer: (3) 1/x + 1/(5z) = 1/(3y)

   उत्तर: (3) 1/x + 1/(5z) = 1/(3y)

   Let a^(2x) = b^(3y) = c^(5z) = k, so a = k^(1/(2x)), b = k^(1/(3y)) and c = k^(1/(5z)). Then b = a²c gives k^(1/(3y)) = k^(2/(2x) + 1/(5z)), so 1/(3y) = 1/x + 1/(5z).

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