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Circular gears P and Q start rotating at the same time at

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Circular gears P and Q start rotating at the same time at [#permalink] New post 20 Mar 2012, 08:04
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Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15
[Reveal] Spoiler: OA

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Re: Circular Gears [#permalink] New post 20 Mar 2012, 08:11
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enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?


Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let t be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> \frac{10}{60}t+6=\frac{40}{60}t --> t=12.

Answer: D.

Hope it's clear.
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post 01 Jul 2012, 02:55
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(40-10)*t=6

t=1/5 mins

(1/5)*60=12 sec
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post 18 Apr 2013, 08:28
I used the following approach:

Circular P has 10rpm >> Therefore one rotation will be every 10/60 seconds

Circular Q has 40rpm >> Therefore one rotation will be every 40/60 seconds


Now we are asked after how many seconds will circular Q have made 6 more rotations than Circular P. Translating into algebra

4/6S-1/6(S)=6

Solve for S (where s is number of seconds)
S=12
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post 25 Oct 2013, 22:48
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enigma123 wrote:
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15



Work done by Faster gear Q is 6 more than slower gear P in same time

i.e W(q) = W(p) + 6
Rq X t = Rp X t + 6
40t=10t + 6
30t = 6
t =1/5 hrs
t = 12 mins
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Re: Circular Gears [#permalink] New post 21 Nov 2013, 00:54
Bunuel wrote:
enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?


Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let t be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> \frac{10}{60}t+6=\frac{40}{60}t --> t=12.

Answer: D.

Hope it's clear.


Is there any theory for this?

I remember from college days, the Key point in solving is that the tangential Velocity should be same at the point of contact?
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post 21 Nov 2013, 01:42
My approach was the following (similar to what LalaB wrote):

Difference between gears Q and P is 30 revolutions per min (40-10).
To make 6 more rotations, the faster gear needs (6 rev / 30 rev/min = 1/5 min). Translate to seconds: 1/5 x 60 = 12.
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post 26 Jan 2014, 22:25
enigma123 wrote:
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15


All the above answers are excellent and I would like to one little tweak that has helped me in quite a few number of Quant problems. This is applicable for people who love to find answers by plugging in the options given

As soon as you arrive at the 2 numbers "6 seconds and 1.5 seconds" (Time taken to complete one rotation) , look at the options given. The best options(9 out of 10 times) are the ones that are a multiple of the above two numbers. Hence you will possibly start with option A and then move to option B and voila.

NOTE: Use this method in scenarios such as this example wherein the number of options that fall under the "multiple umbrella"are quite low. If all the options are multiples it is better to switch on to one of the above strategies.
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Re: Circular gears P and Q start rotating at the same time at [#permalink] New post 22 Jul 2014, 10:33
----RATE-----time--------distance
P:---10 -----x/10------------ x
Q:---40------(x+6)/40-------x+6

The time should be equal, so we solve x/10 = (x+6)/40
x=2

so time = 2/10 min = 12 sec
Re: Circular gears P and Q start rotating at the same time at   [#permalink] 22 Jul 2014, 10:33
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