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Vivek7g
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Wheels of diameters 7cm and 14cm 13 Jun 2016, 19:36
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Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed of the smaller wheel is
A) 22m/s B) 33m/s
C) 44m/s D) 55m/s



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Wheels of diameters 7cm and 14cm 13 Jun 2016, 20:20
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Hi Vivek7g,

To start, when posting PS questions, you should post them in the PS sub-Forum here:

gmat-problem-solving-ps-140/

What is the source of this question? I ask because it's not written in typical GMAT "style." If you're actually studying for the GMAT, then you might want to invest in more realistic practice materials.

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Wheels of diameters 7cm and 14cm 13 Jun 2016, 20:37
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Vivek7g
Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed of the smaller wheel is
A) 22m/s B) 33m/s
C) 44m/s D) 55m/s
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Hi,
Your answers are flawed.....
the Q is talking of cm and answer is given in m/s......
even if I take the smallest speed given, speed = 22m/s or 220cm/s....
so in 10 secs it will travel 220*10 = 2200 cm which alone is MORE than total distance of 1980 cm..

Be careful with the source you are using..

Solution-



Let the # of revolutions be n in 1 sec....
so smaller travels = \(7*pi*n*10 = 70*n*\frac{22}{7}= 220n\)......
bigger travels = \(14*pi*n*10.......140*n*\frac{22}{7} = 440n\)

But total they travel = 1980......... so.\(220n+440n = 1980 ........ n = \frac{1980}{660} = 3\)..
so smaller wheel travels 22*3 cm in 1 secs..... speed = 66 cm/s
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Wheels of diameters 7cm and 14cm 13 Jun 2016, 21:41
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Vivek7g
Wheels of diameters 7cm and 14cm start rolling simultaneously from x & y which are 1980 cm apart towards each other in opposite directions. Both of them make the same number of revolutions per second. If both of them meet after 10seconds.The speed of the smaller wheel is
A) 22m/s B) 33m/s
C) 44m/s D) 55m/s
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Distance covered by wheels in one revolution = their circumference.

Given: Both wheels make same revolutions per sec. say they make x rev/sec.

Circumference of smaller wheel = 2*(22/7)*(7/2) = 22 cm

Circumference of bigger wheel = 2*(22/7)*(14/2) = 44 cm

Distance travelled in one second by smaller wheel: 22x --> Nothing but speed of smaller wheel
Distance travelled in one second by bigger wheel: 44x --> Nothing but speed of bigger wheel

These wheels are moving towards each other. Relative speed: 22x+44x = 66x cm/sec

Total distance reqd to be covered: 1980. Time taken to cover: 10 sec.

(1980/10) = 66x

x = 3

Therefore speed of smaller wheel: 66 cm/sec



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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Thank you for understanding, and happy exploring!
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