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A company sells peanut butter in cylindrical jars. Marketing research

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A company sells peanut butter in cylindrical jars. Marketing research  [#permalink]

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New post 21 Mar 2019, 04:41
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Question Stats:

56% (02:36) correct 44% (02:59) wrong based on 32 sessions

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A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by 25% without altering the volume, by what percent must the height be decreased?


(A) 10
(B) 25
(C) 36
(D) 50
(E) 60

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Re: A company sells peanut butter in cylindrical jars. Marketing research  [#permalink]

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New post 21 Mar 2019, 09:22
Bunuel wrote:
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by 25% without altering the volume, by what percent must the height be decreased?


(A) 10
(B) 25
(C) 36
(D) 50
(E) 60


let intial r=2 ; d=4 & h = 1
vol= pi * 4
after increase diameter 25% ; 1.25*4 = 5 = d = r = 2.5
so vol. 6.25pi
% decrease to be done = 6.25-4/6.25 = 36%
IMO C
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Re: A company sells peanut butter in cylindrical jars. Marketing research  [#permalink]

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New post 24 Mar 2019, 18:31
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Bunuel wrote:
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by 25% without altering the volume, by what percent must the height be decreased?


(A) 10
(B) 25
(C) 36
(D) 50
(E) 60


We can let the initial diameter = 8, so the new diameter = 5/4 x 8 = 10. So the old radius is 4, and the new radius is 5. We can also let the old height = 10, and the new height = h.

Thus, the old volume is:

4^2 x 10 x π = 160π

The new volume is:

5^2 x h x π = 25hπ

Since the two volumes are the same, we can set 25hπ equal to 160π and solve for h:

25hπ = 160π

25h = 160

h = 6.4

Thus, the percent change between the old height and the new height is:

(6.4 - 10)/10 x 100 = (-3.6)/10 x 100 = -36 percent, i.e., a 36 percent decrease

Answer: C
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Re: A company sells peanut butter in cylindrical jars. Marketing research   [#permalink] 24 Mar 2019, 18:31
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