A circular rim 28 inches in diameter rotates the same number

Question

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. \(\frac{48\pi}{x}\)

B. \(75x\)

C. \(48x\)

D. \(24x\)

E. \(\frac{x}{75}\)

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Official Answer

C

A.  \frac{48\pi}{x}

B.  75x

C.  48x

D.  24x

E.  \frac{x}{75}

PS88602.01

Bunuel · Accepted Answer

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. \(\frac{48\pi}{x}\)

B. \(75x\)

C. \(48x\)

D. \(24x\)

E. \(\frac{x}{75}\)

PS88602.01

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Official Answer

C

A. 48pi/x 
B. 75x 
C. 48x 
D. 24x 
E. x/75

1 revolution of a circle = circumference of that circle.

1 revolution of a circle with the diameter of 28 inches =  \pi{d}=28\pi  inches. Hence, x revolutions per second =  28\pi{x}  inches per second =  60*28\pi{x}  inches  per minute .

Given that  60*28\pi{x}=35\pi{n}  -->  n=\frac{60*28\pi{x}}{35\pi}=48x .

Answer: C.

Hope it's clear.

Jaisri · Answer

Understanding the question: 
Note that the question talks about 2 different metrics: 
1) revolution per second which gives the number of revolution made in a second
2) inches per second - which is the distance travelled per second.
It is important to understand these 2 metrics and how they are related.

Facts to refer: 
We know that: Distance travelled = Number of revolutions * Circumference of the circle
Extending that slightly to become rates: Distance travelled per second = Number of revolutions per second * Circumference of the circle.

What's given in the question: 
Inches per second ie., distance per second is equal for 28 inch and 33 inch circles.
Number of revolutions per second by 28 inch = x

What is asked for: 
Number of revolutions per minute by 35 inch = ? Lets have this as variable a. Question asks this in terms of x, so there is no need to solve for x.

Solution: 
Note that 28 inch is in seconds. Since we need the answer in minutes, lets convert that:
Number of revolutions per second by 28 inch = x*60
Applying the earlier stated formula: Distance travelled per second = Number of revolutions per second * Circumference of the circle, we have:
x*60*28*pi=a*35*pi
Solving this equation yields a= 48x.

rohit929 · Answer

circumference * (rev/min) of 28 =circumference * (rev/min) of 35
to calculate z
pi*28*x=pi*35*z
z=4/5 * x
but this is inch/sec we want inch/min

z=4/5 * x*60
=48x

C

sudiptak · Answer

let's say no. of revolution made by the larger rim = n/sec
28 *pi*x= 35*pi*n
therefore, n= (28*pi*x)/(35*pi)=4x/5
so in 1 min no of revolution = 60*(4x/5)=48x

so C

honchos · Answer

1 revolution of a circle with the diameter of 28 inches = \pi{d}=28\pi inches. Hence, x revolutions per second = 28\pi{x} inches per second = 60*28\pi{x} inches per minute.

Couldn't understand why 60 has come into picture?

Bunuel · Answer

1 revolution of a circle with the diameter of 28 inches = \pi{d}=28\pi inches. Hence, x revolutions per second = 28\pi{x} inches per second = 60*28\pi{x} inches per minute.

Couldn't understand why 60 has come into picture?

28\pi{x}  inches   per second   =  60*28\pi{x}  inches   per minute  .

honchos · Answer

28\pi{x} inches per second = 60*28\pi{x} inches per minute.

it should be actually divided by 60 to convert it into minutes?

Bunuel · Answer

10 inches per second. There are 60 seconds in minute so 60*10 inches per minute.

b2bt · Answer

I'm still little unclear about how you equalise 60*28pi = 35pi*n
Is it because in the question it says that the inches covered by both the circles in a given time is same

Bunuel · Answer

I'm still little unclear about how you equalise 60*28pi = 35pi*n
Is it because in the question it says that the inches covered by both the circles in a given time is same

Yes.

The smaller rim =  60*28\pi{x}  inches  per minute .
The larger rim =  35\pi{n}  inches  per minute , where n is the number of revolution per minute.

We are told that those two are equal.

Does this make sense?

PareshGmat · Answer

If x = 1, then the options would turn up as follows:

A. 48pi 
B. 75
C. 48 
D. 24 
E. 1/75

Small circle circumference * 1 revolution  = 2\pi * 14 * 1 = 28\pi

Large circle circumference * r revolution = 2\pi * 17.5 * r = 35\pi * r

Given that 35\pi * r = 28\pi

r = \frac{4}{5} \frac{revolutions}{second} = \frac{4}{5} * 60 = 48 \frac{revolutions}{minute}

Answer = C

elizaanne · Answer

One important thing to keep in mind right off the bat is that the smaller rim makes x revolutions per SECOND and they ask for how many revolutions per MINUTE the larger rim makes.

If the two rims rotate the same number of inches per second, then
28(pi)x/sec=35(pi)z/sec (with z being the number of rotations the larger rim makes per second)
so we want to isolate for z and we end up with
28(pi)x/35(pi)(sec)=z/sec
the pi's cancel out and we simplify it to
4/5x however we need to multiply it by 60, because the question asks for minutes, so the answer is 48x (C)

ShashankDave · Answer

Okay..here it goes..

Lets call the smaller one A and the larger one B.

A's diameter =  28 , so circumference =  28\pi 
B's diameter =  35 , so circumference =  35\pi

Let the number of revolutions of A = x, and those of B = y.
According to the question..
 28\pi*x = 35\pi*y

Thus,

y = \frac{4}{5}x

But that's the value of revolutions per second. For per minute..multiply it with 60.

Answer 48x(C).

SVaidyaraman · Answer

1. We will convert x revolutions per second of the smaller rim as 60x revolutions per minute
2. The distance rotated per second is the same for both but since the diameters are different, we know that the larger rim makes lesser revolutions per second
3. The ratio of the number of revolutions of the two rims are given by the inverse of the ratio of their diameters.
4. So the number of revolutions per minute of the larger rim is 60x *(28/35) = 48x.

ScottTargetTestPrep · Answer

The smaller rim rotates at a rate of 28πx inches per second. Since the larger rim rotates the same number of inches per second, it rotates at a rate of 28πx inches per second also, and, in one minute, it rotates 28πx * 60 inches.

Since 1 rotation of the larger rim = its circumference = 35π, the number of rotations made by the larger rim will thus be:

(28πx * 60)/35π

(4x * 60)/ 5

4x * 12

48x

Answer: C

nishantkurup · Answer

Concept to first understand: With 1 revolution, a rim will travel the distance equal to that of its circumference. (Think about it)

Small Rim  
Diameter = 28
Circumference = 28Pi
In 1 second, it makes x revolutions, so distance traveled = 28Pi(x)...........(1)

Large rim  
Diameter = 35
Circumference = 35Pi
Assume in 1 second, it makes 'n' revolutions, so distance traveled = 35Pi(n)..........(2)

Now, the question says that the larger rim travels the same distance as the smaller rim per second (i.e; rotates the same number of inches). Thus, when you equate equations (1) and (2) - you get Number of revolutions by large rim (n) in terms of number of revolutions by the small rim (x)  in 1 second .

35Pi(n) = 28Pi(x)
 n = 4x/5 (per second)

Therefore in a minute, the larger rim makes 60n revolutions = (4x/5) * 60 = 48x

Hence the answer is C: 48x

kskumar · Answer

avigutman  could you please explain how to Eliminate answer choices using units?

100mitra · Answer

Option C : 48
Simple = (28/35)*60 sec = 48 (Ratio and Proportion)

avigutman · Answer

x has units of revolutions per second, and the correct answer should have units of revolutions per minute per the question. In both cases we are looking at the following ratio: 
 revolutions : time 
The units of answer choice A are the reciprocal of what we want (because x is in the denominator), so it can be eliminated. The other answer choices are okay as far as their units are concerned.

A circular rim 28 inches in diameter rotates the same number

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