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

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Manager
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A cask is filled with a mixture of 2 liquids A and B in the [#permalink]

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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
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21 Jul 2003, 22:12
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
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22 Jul 2003, 08:01
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.
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22 Jul 2003, 15:41

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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Re: A cask is filled with a mixture of 2 liquids A and B in the [#permalink]

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08 Sep 2016, 05:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A cask is filled with a mixture of 2 liquids A and B in the   [#permalink] 08 Sep 2016, 05:45
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