Grade 11Algebra

If the ratio of H.M and G.M of two numbers is 12:13 , then the ratio of the numbers is?

Question image for If the ratio of H.M and G.M of two numbers is 12:1

Piyush Upadhyay

8 Years agoGrade 11

1 Answer

Khimraj

8 Years ago

Let numbers are a and b. then

HM = 2ab/(a+b)

GM = $\sqrt{ab}$

HM/GM = 12/13

2 $\sqrt{ab}$ /(a+b) = 12/13

(a+b)/ $\sqrt{ab}$ = 13/6

$\sqrt{a/b}$ + $\sqrt{b/a}$ = 13/6

Let $\sqrt{a/b}$ = x.then

x + 1/x = 13/6

6x² – 13x + 1=0

x = 2/3 or 3/2

a/b = x² = 4/9 or 9/4.

So correct option is (D) 4/9.

Hope it clears. If you like answer then please approve it.

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View all Questions

If the ratio of H.M and G.M of two numbers is 12:13 , then the ratio of the numbers is?

Piyush Upadhyay

1 Answer

Khimraj

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