Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Two Numbers Whose A.M. is 25 and Gm is 20. - Mathematics

Find the two numbers whose A.M. is 25 and GM is 20.

#### Solution

$\text { Let A . M . and G . M . between the two numbers a and b be A and G, respectively } .$

$A = 25$

$\Rightarrow \frac{a + b}{2} = 25$

$\Rightarrow a + b = 50 . . . . . . . (i)$

$\text { Also } G = 20$

$\Rightarrow \sqrt{ab} = 20$

$\Rightarrow ab = 400 . . . . . . . (ii)$

$\text { Now, putting the value of a in } (ii):$

$\Rightarrow (50 - b)b = 400$

$\Rightarrow b^2 - 50b + 400 = 0$

$\Rightarrow b^2 - 10b - 40b + 400 = 0$

$\Rightarrow b\left( b - 10 \right) - 40\left( b - 10 \right) = 0$

$\Rightarrow \left( b - 10 \right)\left( b - 40 \right) = 0$

$\Rightarrow b = 10, 40$

$\text { If }b = 10, \text { then }, a = 400 .$

$\text { And , if b = 40, then a } = 10 .$

$\text { Thus, the two numbers are 10 and 40 } .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Exercise 20.6 | Q 6 | Page 55