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A smaller circular rim 24 inches in diameter rotates the same number

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Joined: 02 Sep 2009
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A smaller circular rim 24 inches in diameter rotates the same number  [#permalink]

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New post 16 Oct 2018, 04:43
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Difficulty:

  55% (hard)

Question Stats:

57% (01:39) correct 43% (02:31) wrong based on 38 sessions

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A smaller circular rim 24 inches in diameter rotates the same number of inches per second as a larger circular rim 36 inches in diameter. If the smaller rim makes r revolutions per second, how many revolutions per second does the larger rim make in terms of r ?


(A) 3r/2

(B) 4r/9

(C) 2r/3

(D) 9r/4

(E) r/3

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Re: A smaller circular rim 24 inches in diameter rotates the same number  [#permalink]

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New post 16 Oct 2018, 05:09
1
Distance covered by smaller circle in 1 second=24π×r(revolutions per sec)
Distance covered by Bigger circle in 1 second=36π×a(let a be number of revolutions of Bigger circle in 1 sec)

Both distance are same
Therefore
24πr=36πa
a=2r/3

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Re: A smaller circular rim 24 inches in diameter rotates the same number  [#permalink]

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New post 16 Oct 2018, 05:55
Let the small rim perform 1 revolution in 1 sec
If the smaller rim covers 24π inch in 1 sec , larger rim covers 24π as well.
But the larger rim needs to cover 36π for 1 revolution.
Therefore revolution for larger rim is 24πr/36π = 2r/3
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Re: A smaller circular rim 24 inches in diameter rotates the same number   [#permalink] 16 Oct 2018, 05:55
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A smaller circular rim 24 inches in diameter rotates the same number

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