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A tractor has a front wheel diameter of h cm and rear wheel diameter

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A tractor has a front wheel diameter of h cm and rear wheel diameter  [#permalink]

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New post Updated on: 18 Jul 2018, 07:54
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A
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E

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  35% (medium)

Question Stats:

70% (01:33) correct 30% (01:24) wrong based on 37 sessions

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A tractor has a front wheel diameter of h cm and rear wheel diameter of k cm. The front wheel covers a distance of m meters in 1000 revolutions. How many revolutions does the rear wheel make in covering m meters?

A. 1000h/k
B. 1000k - h
C. 1000hk
D. 1000h - k
E. 1000k/h

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Originally posted by Harshgmat on 18 Jul 2018, 07:52.
Last edited by Bunuel on 18 Jul 2018, 07:54, edited 1 time in total.
Renamed the topic.
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Re: A tractor has a front wheel diameter of h cm and rear wheel diameter  [#permalink]

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New post 18 Jul 2018, 08:07
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1
Harshgmat wrote:
A tractor has a front wheel diameter of h cm and rear wheel diameter of k cm. The front wheel covers a distance of m meters in 1000 revolutions. How many revolutions does the rear wheel make in covering m meters?

A. 1000h/k
B. 1000k - h
C. 1000hk
D. 1000h - k
E. 1000k/h


Since both the wheels belong to the same vehicle hence at any time the distance travelled by both the wheels should be equal

i.e. Distance of wheel 1 = Distance pf wheel 2

i.e. Circumference*Number of revolutions of wheel 1 = Circumference*Number of revolutions of wheel 2

i.e. Diameter*Number of revolutions of wheel 1 = Diameter*Number of revolutions of wheel 2

i.e. h*1000 = k*Revolutions

i.e. Revolutions of wheel 2 = h*1000/k

Answer: option A
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Re: A tractor has a front wheel diameter of h cm and rear wheel diameter  [#permalink]

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New post 18 Jul 2018, 08:17
Harshgmat wrote:
A tractor has a front wheel diameter of h cm and rear wheel diameter of k cm. The front wheel covers a distance of m meters in 1000 revolutions. How many revolutions does the rear wheel make in covering m meters?

A. 1000h/k
B. 1000k - h
C. 1000hk
D. 1000h - k
E. 1000k/h



The revolution would depend on the circumference..
Let the dia h be twice of k.......h=2k
Since role of dia is a linear function in circumference, that is \(\pi*dia\)
If h takes 1000 revolution to cover m meter, k will take 2000 as k is half of h..
Look for choice that gives 2000 by substituting h =2k
Only A and E will remove variables..
A. 1000h/k....1000*2k/k=2000....... YES
E. 1000k/h...... 1000*k/2k=500......No

Ans A
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Re: A tractor has a front wheel diameter of h cm and rear wheel diameter  [#permalink]

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New post 22 Jul 2018, 18:07
Harshgmat wrote:
A tractor has a front wheel diameter of h cm and rear wheel diameter of k cm. The front wheel covers a distance of m meters in 1000 revolutions. How many revolutions does the rear wheel make in covering m meters?

A. 1000h/k
B. 1000k - h
C. 1000hk
D. 1000h - k
E. 1000k/h


The circumference of the front wheel is hπ and that of the rear wheel is kπ. The number of revolutions of a wheel to cover a distance is equal to the distance divided by the circumference of the wheel; thus, we see that m/(hπ) = 1000 or m = 1000hπ. Therefore, the number of revolution the rear wheel makes is

m/(kπ) = 1000hπ/kπ = 1000h/k

Answer: A
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Re: A tractor has a front wheel diameter of h cm and rear wheel diameter &nbs [#permalink] 22 Jul 2018, 18:07
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