UPSC CAPF (AC) 2024 Paper I · Question 50

Question 50 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 · Q50 · General Mental Ability · Arithmetic

   The ratio of present ages (in years) of X to Y is equal to the ratio of present ages (in years) of Y to Z. If the present age of Y is 15 years, then which of the following can be the sum of the ages (in years) of X, Y and Z?

   1. 35
   2. 40
   3. 49
   4. 55

   X और Y की वर्तमान आयु (वर्षों में) का अनुपात Y और Z की वर्तमान आयु (वर्षों में) के अनुपात के बराबर है। यदि Y की वर्तमान आयु 15 वर्ष है, तो निम्नलिखित में से कौन-सा X, Y और Z की आयु (वर्षों में) का योगफल हो सकता है?

   1. 35
   2. 40
   3. 49
   4. 55
   Show answer

   Answer: (3) 49

   उत्तर: (3) 49

   X : Y = Y : Z gives XZ = 15² = 225, so X + Z is at least 2√225 = 30 and the total is at least 45, ruling out 35 and 40. With whole-number ages the pairs with product 225 are (1, 225), (3, 75), (5, 45), (9, 25) and (15, 15), giving totals of 241, 93, 65, 49 and 45, so 49 (ages 9, 15 and 25) is the answer; 55 would need ages that are not whole numbers.

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