Central Tendency & DispersionMTP June 24 Series IIQuestion 3070 of 473
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The Arithmetic Mean between two numbers is 15\displaystyle 15 and their G.M. is 9\displaystyle 9; then the numbers are −\displaystyle -

Options

A27,3\displaystyle 27, 3
B9,9\displaystyle 9, 9
C16,9\displaystyle 16, 9
DNone of these
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Correct Answer

✅ Option a — 27,3\displaystyle 27, 3

All Options:

  • A27,3\displaystyle 27, 3
  • B9,9\displaystyle 9, 9
  • C16,9\displaystyle 16, 9
  • DNone of these

Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be a\displaystyle a and b\displaystyle b. a+b2=15⇒a+b=30\frac{a+b}{2} = 15 \Rightarrow a + b = 30 ab=9⇒ab=81\sqrt{ab} = 9 \Rightarrow ab = 81 **Step 2: Solve.** (a−b)2=(a+b)2−4ab=900−324=576(a-b)^2 = (a+b)^2 - 4ab = 900 - 324 = 576 ∣a−b∣=24|a-b| = 24 From a+b=30\displaystyle a + b = 30 and a−b=24\displaystyle a - b = 24: a=30+242=27,b=30−242=3a = \frac{30+24}{2} = 27, \quad b = \frac{30-24}{2} = 3 **Verification:** - AM = (27+3)/2=15\displaystyle (27+3)/2 = 15 ✓ - GM = 27×3=81=9\displaystyle \sqrt{27 \times 3} = \sqrt{81} = 9 ✓ Hence, **Option A** is the correct answer.

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