If the AM & GM of two numbers are 30 and 24 respectively. Find the no's.

Option b: 48 and 12. Solution: Step 1: Set up equations. Let the two numbers be a and b. a+b/2 = 30 Rightarrow a + b = 60 sqrt(ab) = 24 Rightarrow ab = 576 Step 2: Solve for a and b. (a-b)^2 = (a+b)^2 - 4ab = 3600 - 2304 = 1296 |a-b| = 36 From a + b = 60 and a - b = 36: 2a = 96 Rightarrow a = 48, quad b = 12 Verification: - AM = (48+12)/2 = 30 ✓ - GM = sqrt(48 x 12) = sqrt(576) = 24 ✓ So the numbers are 48 and 12 = Option B. Note: The exam key says D (40 and 20), but AM of 40 and 20 = 30 ✓, GM = sqrt(800) !=q 24. The correct answer is B (48 and 12). Hence, Option B is the correct answer.

Central Tendency & DispersionPYQ Nov 24Question 3029 of 473

All Questions

If the AM & GM of two numbers are $\displaystyle 30$ and $\displaystyle 24$ respectively. Find the no's.

Options

\displaystyle 12

and

\displaystyle 24

\displaystyle 48

and

\displaystyle 12

\displaystyle 30

and

\displaystyle 20

\displaystyle 40

and

\displaystyle 20

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Correct Answer

✅ Option b — $\displaystyle 48$ and $\displaystyle 12$

All Options:

A $\displaystyle 12$ and $\displaystyle 24$
B $\displaystyle 48$ and $\displaystyle 12$
C $\displaystyle 30$ and $\displaystyle 20$
D $\displaystyle 40$ and $\displaystyle 20$

Detailed Solution & Explanation

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

\displaystyle a

and

\displaystyle b

\frac{a+b}{2} = 30 \Rightarrow a + b = 60

\sqrt{ab} = 24 \Rightarrow ab = 576

**Step 2: Solve for

\displaystyle a

and

\displaystyle b

.**

\displaystyle (a-b)^2 = (a+b)^2 - 4ab = 3600 - 2304 = 1296

|a-b| = 36

From

\displaystyle a + b = 60

and

\displaystyle a - b = 36

2a = 96 \Rightarrow a = 48, \quad b = 12

**Verification:** - AM =

\displaystyle (48+12)/2 = 30

✓ - GM =

\displaystyle \sqrt{48 \times 12} = \sqrt{576} = 24

✓ So the numbers are

\displaystyle 48

and

\displaystyle 12

= **Option B**. Note: The exam key says D (

\displaystyle 40

and

\displaystyle 20

), but AM of 40 and 20 = 30 ✓, GM =

\displaystyle \sqrt{800} \neq 24

. The correct answer is **B** (

\displaystyle 48

and

\displaystyle 12

). Hence, **Option B** is the correct answer.

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If the AM & GM of two numbers are 30\displaystyle 3030 and 24\displaystyle 2424 respectively. Find the no's.