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NDA 2017 Maths · Mathematics · Sequences and Series · hard

The arithmetic mean of two positive numbers is 5/4 times their geometric mean. The ratio of the larger to the smaller number is

Single correct option

The arithmetic mean of two positive numbers is 54\dfrac54 times their geometric mean. The ratio of the larger to the smaller number is
  1. A. 2:12:1
  2. B. 5:25:2
  3. C. 9:49:4
  4. D. 4:14:1
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Answer: (D) 4:14:1

Let the numbers be aa and bb with t=a/bt=a/b. t+12t=54⇒2t−5t+2=0⇒t=2\frac{t+1}{2\sqrt t}=\frac54\Rightarrow2t-5\sqrt t+2=0\Rightarrow\sqrt t=2 or 12\frac12, so t=4t=4 (or 14\frac14). The ratio is 4:14:1. Option 2:12:1 is the ratio of the square roots.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake