As shown in the figure above, a cylindrical oil tank is i full. If 3 : Problem Solving (PS)

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As shown in the figure above, a cylindrical oil tank is i full. If 3

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Math Expert

Joined: 02 Sep 2009

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As shown in the figure above, a cylindrical oil tank is i full. If 3 [#permalink]

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08 Feb 2018, 04:38

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As shown in the figure above, a cylindrical oil tank is i full. If 3 more gallons are added, the tank will be half full. What is the capacity, in gallons, of the tank?

(A) 15
(B) 16
(C) 17
(D) 18
(E) 19

Spoiler: ::

Attachment:

2018-02-08_1636.png [ 7.29 KiB | Viewed 840 times ]

Spoiler: OA

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Re: As shown in the figure above, a cylindrical oil tank is i full. If 3 [#permalink]

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08 Feb 2018, 04:44

1/3x+3=1/2x
X+9/3=1/2x
2x+18=3x
X=18

Ans D

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Re: As shown in the figure above, a cylindrical oil tank is i full. If 3 [#permalink]

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08 Feb 2018, 06:03

3 gallons is equal to 1/2 - 1/3 = 1/6 of the total capacity of the tank

Therefore capacity of the tank is 3 / (1/6) = 18 gallons

=> Answer D

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Re: As shown in the figure above, a cylindrical oil tank is i full. If 3 [#permalink]

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04 Oct 2018, 08:53

Bunuel wrote:

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Attachment:

2018-02-08_1636.png

Dear Moderator,
There seems to be a small typo here , instead of 1/3 , only letter "i" can come up, hope you will do the needful. Thank you.
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Re: As shown in the figure above, a cylindrical oil tank is i full. If 3 [#permalink]

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04 Oct 2018, 10:29

A cylindrical oil tank is 1/3 means current volume =1/3V

3 gallons added to the existing 1/3 it becomes half =>$1/3V+3=1/2V$

What is the capacity, in gallons, of the tank?
Solving for $1/3V+3=1/2V$

$1/6v=3$

volume=18 so D

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Re: As shown in the figure above, a cylindrical oil tank is i full. If 3 [#permalink]

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07 Oct 2018, 18:24

Bunuel wrote:

Spoiler: ::

Attachment:

2018-02-08_1636.png

We can let n = the total capacity and create the equation:

n/3 + 3 = n/2

Multiplying by 6 we have:

2n + 18 = 3n

18 = n

Alternate Solution:

The amount of oil in the tank increases from 1/3 to 1/2, which is 1/2 - 1/3 = 3/6 - 2/6 = 1/6 of the tank, and this is equal to 3 gallons. We see that if 3 gallons is 1/6 of the tank’s capacity, then 3 x 6 = 18 gallons is the tank’s total capacity.

Answer: D
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