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A circular rim A having a diameter of 28 inches is rotating

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A circular rim A having a diameter of 28 inches is rotating  [#permalink]

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New post Updated on: 17 Aug 2013, 02:44
3
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A
B
C
D
E

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  25% (medium)

Question Stats:

79% (01:59) correct 21% (01:56) wrong based on 138 sessions

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A circular rim A having a diameter of 28 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 35 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.

A) 5x/4
B) 4x/5
C) 7x/5
D) 5x/7
E) 3x/4

Originally posted by pjagadish27 on 16 Aug 2013, 09:50.
Last edited by Bunuel on 17 Aug 2013, 02:44, edited 1 time in total.
RENAMED THE TOPIC.
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Re: Relative Motion  [#permalink]

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New post 16 Aug 2013, 10:14
pjagadish27 wrote:
A circular rim A having a diameter of 28 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 35 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.

A)5x/4
B)4x/5
C)7x/5
D)5x/7
E)3x/4


since both the rims reach their starting positions at the same time after every rotation.
==>this means time to rotate 1 revolution for both are same.
time = distance/speed
distance = perimeter of each circle

now perimeter of circle with dia \(28 = 28 pi\)
speed = \(x\)
therefore time = \(\frac{28 pi}{x}\)

now perimeter of circle with dia \(35 = 35 pi\)
speed =\(y\)
therefore time =\(\frac{35 pi}{y}\)

now since both times are equal therefore: \(\frac{35 pi}{y} = \frac{28 pi}{x}\)

on solving \(y = \frac{5x}{4}\)

hence A
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Re: A circular rim A having a diameter of 28 inches is rotating  [#permalink]

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New post 18 Aug 2013, 21:28
Consider a point on each of the rims , now this point will cover full rotation in same time for both the rims.

So,

Rate * Time = Distance = Circumference

x*t = 2*pi*14 ... -(1)
y*t = 2*pi*17.5 .... - (2).

(2)/(1) => (y/x) = 175/140

Hence y= x*(5/4)
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Re: A circular rim A having a diameter of 28 inches is rotating  [#permalink]

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New post 19 Aug 2013, 04:02
pjagadish27 wrote:
A circular rim A having a diameter of 28 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 35 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.

A) 5x/4
B) 4x/5
C) 7x/5
D) 5x/7
E) 3x/4


t = S1/V1 = S2/V2
or, 28/x = 35/y
or, y = 35x/28 = 5x/4 (Answer A)
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Re: A circular rim A having a diameter of 28 inches is rotating  [#permalink]

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New post 14 Jan 2019, 19:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A circular rim A having a diameter of 28 inches is rotating   [#permalink] 14 Jan 2019, 19:01
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