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# A cask is filled with a mixture of 2 liquids A and B in the

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Manager
Joined: 08 Apr 2003
Posts: 149
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A cask is filled with a mixture of 2 liquids A and B in the [#permalink]  21 Jul 2003, 17:32
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A cask is filled with a mixture of 2 liquids A and B in the proportion A:B :: 5:3. When 16 gallons of the mixture are drawn off and the acsk filled with liquid B the proportion become A:B:: 3:5. How many gallons does the cask hold?
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

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initially, X gallons is the capacity

liquid A) 5X/8 - five parts out of 8 given
liquid B) 3X/8

-16 gallons of mixture (according to the initial proportion of 5/3)

liquid A) 5X/8 - 10
liquid B) 3X/8 - 6

+16 gallons of liquid B

liquid A) 5X/8 - 10
liquid B) 3X/8 - 6 +16 = 3X/8 +10

A new proportion

5X/8 - 10
------------ = 3/5
3X/8 +10

solve for X, X=40
Manager
Joined: 10 Jun 2003
Posts: 210
Location: Maryland
Followers: 2

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Sure, 40 is the answer. Just to share how i did this, made a table with two columns, one for substance A and and for B. I started with the known (16 gal of B) then added the mixture until I saw the correct ratio:

A B
0 16
5 19
10 22
15 25

We see that 15 and 25 are in 3:5 ratio and add up to 40. Perhaps this is not the cleanest way, and definitely would not work for "messy" numbers, but as the GMAT is generally clean, it is OK here.
Manager
Joined: 08 Apr 2003
Posts: 149
Followers: 1

Kudos [?]: 11 [0], given: 0

mciatto wrote:
Sure, 40 is the answer. Just to share how i did this, made a table with two columns, one for substance A and and for B. I started with the known (16 gal of B) then added the mixture until I saw the correct ratio:

A B
0 16
5 19
10 22
15 25

We see that 15 and 25 are in 3:5 ratio and add up to 40. Perhaps this is not the cleanest way, and definitely would not work for "messy" numbers, but as the GMAT is generally clean, it is OK here.

Perhaps gambling with iterations..

Anyways i feel one should choose a method which suits him the best.

As to more algebraic approach, Stolyar has the solution posted for you.
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# A cask is filled with a mixture of 2 liquids A and B in the

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