A wheel has a diameter of x inches and a second wheel has a diameter

Question

A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

Kudos for a correct solution.

A. 100xy 
B. 100y - x 
C. 100x - y 
D. 100y/x 
E. 100x/y

Kudos for a correct  solution .

chandan276 · Accepted Answer

A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?

A. 100xy
B. 100y - x
C. 100x - y
D. 100y/x
E. 100x/y

Kudos for a correct solution.

A. 100xy 
B. 100y - x 
C. 100x - y 
D. 100y/x 
E. 100x/y

First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)

Now,
Revolutions = distance/circumference

So, from equation (1)
100 = d/(x*pi) 
d = 100 * x * pi ---------- (3)

From equation (2)
Revolutions = d/(y*pi) = (100 * x * pi) / (y*pi) = 100x/y

Answer (E)

82vkgmat · Answer

d feet = 12d inches = 100 revolutions = 100*circumference = 100*(pi)*x
For same distance # revolutions for second wheel = distance/circumference = 100*pi*x/(pi*y) = 100x/y.

Answer E.

PareshGmat · Answer

Answer = E. 100x/y

............................ Wheel A ..................... Wheel B

Diameter .................. x .............................. y

Radius ....................  \frac{x}{2}  ............................  \frac{y}{2}

Circumference ..........  \frac{d}{100}  .........................  2\pi(\frac{y}{2})  .............

2\pi(\frac{x}{2}) = \frac{d}{100}

d = 100\pi x

Revolutions of Wheel B to achieve distance d = \frac{100\pi x}{2\pi(\frac{y}{2})} = 100\frac{x}{y}

KarishmaParmar · Answer

A very simple Question Circumference of a circle = pi * D = distance covered in one revolution. For first circle, one revolution = pi*x In 100 revolutions, distance covered = 100* pi*x = d feet Second wheel in one revolution = pi*y For d feet or for 100*pi*x it will take 100*pi*x / pi*y or, 100x/y Answer E My Kudos Please :oops:

Abhishek009 · Answer

So,  d  =  100*2π*\frac{x}{4}

Circumference of the second wheel is  2π*\frac{y}{4}

=>  (100*2π*x/4) / (2π*y/4)

=>  \frac{100x}{y}

Hence answer will be (E)  \frac{100x}{y}

babuvgmat · Answer

A wheel covers 2πr distance in one revolution. where r= diameter/2

First wheel covers d feet in 100 rev. => d= 100* 2π * (x/2)

Second wheel covers d feet in let's say P revolutions; => d = P* 2π * (y/2)

comparing both equations:-

=> p= (100∗2π∗x/2)/(2π∗y/2)

=> 100x/y

OA :- E

JeffTargetTestPrep · Answer

Recall that d feet = 12d inches and the circumference (C = 2πr or Dπ) of the x-inch diameter wheel = xπ and that of the y-inch diameter wheel = yπ.

Therefore, we know that in 1 revolution, the first wheel covers a distance of xπ inches. Thus, in 100 revolutions, it covers 12d inches, as shown here:
xπ * 100 = 12d

If we let r = the number of revolutions the second wheel makes, we have:

yπ * r = 12d

Thus, we have:

xπ * 100 = yπ * r

100x = yr

100x/y = r

Answer: E

KarishmaB · Answer

Distance travelled is the same in both cases.

Distance = Circumference of wheel * No of revolutions  = 2*\pi*x/2 * 100 = 2*\pi*y/2 * R 
R = 100x/y

Answer (E)

Note that we don't need to worry about different units because they will all cancel off anyway.

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A wheel has a diameter of x inches and a second wheel has a diameter

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