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# Two interconnected, circular gears travel at the same circumferential

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Math Expert
Joined: 02 Sep 2009
Posts: 49251
Two interconnected, circular gears travel at the same circumferential  [#permalink]

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21 Jul 2016, 04:46
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65% (hard)

Question Stats:

50% (00:56) correct 50% (01:04) wrong based on 296 sessions

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Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 30 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?

(A) 3:5

(B) 9:25

(C) 5:3

(D) 25:9

(E) Cannot be determined from the information provided

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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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21 Jul 2016, 05:51
1
the bigger the diameter, the more distance wheel covers per revolutions OR lesser the revolutions wheel takes to cover the same distance. Going by this, rev. is inversely proportional to the diameter. Hence, $$\frac{(rev. of A)}{(rev. of B)}$$ =$$\frac{(diameter of B)}{(diameter of A)} =\frac{3}{5}$$
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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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21 Jul 2016, 09:48
Bunuel wrote:
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 30 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?

(A) 3:5

(B) 9:25

(C) 5:3

(D) 25:9

(E) Cannot be determined from the information provided

Distance covered by A=2*pi*r--------->30*pi
Distance covered by B=2*pi*r--------->50*pi
since their rates are equal
ratio=30*pi/50*pi==3/5
Ans A
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Two interconnected, circular gears travel at the same circumferential  [#permalink]

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21 Jul 2016, 20:23
A rpm*30⫪=B rpm*50⫪
A rpm/B rpm=50⫪/30⫪=5/3
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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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21 Jul 2016, 22:02
Bunuel wrote:
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 30 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?

(A) 3:5

(B) 9:25

(C) 5:3

(D) 25:9

(E) Cannot be determined from the information provided

Smaller the diameter, more the number of revolutions made since the circumferential rate of travel is the same for both gears (this just means that they cross the same distance in the given time). So smaller diameter means smaller circumference and hence more complete circles of travel.
Circumference of A/Circumference of B = Number of revolutions of B/Number of revolutions of A

Number of revolutions of B/Number of revolutions of A $$= 30\pi/50\pi$$

Number of revolutions of A/Number of revolutions of B = 5/3

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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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21 Jul 2016, 22:16
2
Bunuel wrote:
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 30 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?

(A) 3:5

(B) 9:25

(C) 5:3

(D) 25:9

(E) Cannot be determined from the information provided

Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B

Time A = 2*pi*25/Speed A
Time B = 2*pi*15/Speed B

Since the times are same,

50pi/Speed A = 30pi/Speed B
SpeedA/Speed B = 50pi/30pi = 5/3

Correct Option: C
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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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27 Oct 2017, 02:25
it is given that rate is same i.e. the distance covered by A & B is same i.e.
Distance=circumference*revolution
so we can derive this relation

30*A=50*B (pie is canceled out)
A/B= 5/3
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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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30 Oct 2017, 14:07
Bunuel wrote:
Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 30 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?

(A) 3:5

(B) 9:25

(C) 5:3

(D) 25:9

(E) Cannot be determined from the information provided

We see that Gear A has a circumference of 30π and Gear B has a circumference of 50π.

Since Gear A will make more revolutions than Gear B, the ratio is 50π/30π = 5/3.

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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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30 Oct 2017, 21:59
The circumference of circle = 2*Pi*r
here 2*pi constant
the number of revolution A should be more
hence it should be 5:3
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Re: Two interconnected, circular gears travel at the same circumferential  [#permalink]

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31 Oct 2017, 03:29
Both gears travel at the same rate x centimeter/min
Gear A travel x centimeters = x/30 revolution per minute
Grear B travel x centimeters = x/50 revolutions per minute
=> Ratio = (x/30)/(x/50) = 5:3
Hope it clears
Re: Two interconnected, circular gears travel at the same circumferential &nbs [#permalink] 31 Oct 2017, 03:29
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