The Arithmetic Mean between two numbers is 15 and their G.M. is 9 ; then the numbers are -

Option a: 27, 3. Solution: Step 1: Set up equations. Let the two numbers be a and b . a+b/2 = 15 ⟹ a + b = 30 sqrt(ab) = 9 ⟹ ab = 81 Step 2: Solve. (a-b)2 = (a+b)2 - 4ab = 900 - 324 = 576 |a-b| = 24 From a + b = 30 and a - b = 24 : a = 30+24/2 = 27, b = 30-24/2 = 3 Verification: - AM = (27+3)/2 = 15 ✓ - GM = sqrt(27 × 3) = sqrt(81) = 9 ✓ Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 3070 of 473

All Questions

The Arithmetic Mean between two numbers is $\displaystyle 15$ and their G.M. is $\displaystyle 9$ ; then the numbers are $\displaystyle -$

Options

\displaystyle 27, 3

\displaystyle 9, 9

\displaystyle 16, 9

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 27, 3$

All Options:

A $\displaystyle 27, 3$
B $\displaystyle 9, 9$
C $\displaystyle 16, 9$
DNone of these

Detailed Solution & Explanation

**Step 1: Set up equations.** Let the two numbers be

\displaystyle a

and

\displaystyle b

\frac{a+b}{2} = 15 \Rightarrow a + b = 30

\sqrt{ab} = 9 \Rightarrow ab = 81

**Step 2: Solve.**

(a-b)^2 = (a+b)^2 - 4ab = 900 - 324 = 576

|a-b| = 24

From

\displaystyle a + b = 30

and

\displaystyle a - b = 24

a = \frac{30+24}{2} = 27, \quad b = \frac{30-24}{2} = 3

**Verification:** - AM =

\displaystyle (27+3)/2 = 15

✓ - GM =

\displaystyle \sqrt{27 \times 3} = \sqrt{81} = 9

✓ Hence, **Option A** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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The Arithmetic Mean between two numbers is 15\displaystyle 1515 and their G.M. is 9\displaystyle 99; then the numbers are −\displaystyle -−