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# A dishonest milkman sells a 40 liter mixture of milk and water that co

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Math Expert
Joined: 02 Sep 2009
Posts: 46297
A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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28 Jan 2015, 07:53
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25% (medium)

Question Stats:

83% (01:48) correct 17% (02:29) wrong based on 229 sessions

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A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.

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Posts: 5938
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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28 Jan 2015, 08:17
1
ans C 2:3...
initial 40 ltrs ... when 20 ltr left m:w=3:2=12:8..
now 20l removed, means half of each left=16:4..
now add 20 l water m:w=16:24=2:3
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Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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28 Jan 2015, 08:38
3
Here we go:

Quantity of mixture = 40

Lets divide the whole process into three steps.

Step 1:
Milk:Water = 3:2

Milk = 24
Water = 16

Step 2:
He takes out 20 liters of the mixture and replaces it with an equal amount of milk.

Quantity of milk = 20 + 3/5 * (20) = 32
Water = 40 - 32 = 8

New ratio

Milk:Water = 4:1

Step 3:
He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture.

Quantity of water = 20 + 1/5 * (20) = 24
Milk = 40 - 24 = 16

Ration in the final mixture

Milk:Water = 16:24 = 2:3

Option C is correct
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Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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28 Jan 2015, 22:34
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.

C: 2:3

I took the long route.. i would like to solve this algebraically.. I am pondering over that now...
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Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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29 Jan 2015, 00:03
4
Hi maxk297,

While many ratio questions can be solved by setting up an algebraic equation, this really isn't one of those questions. It's pure Arithmetic - we're given the starting numbers, we're told what to add and subtract, and then we're asked for an end result. In that way, this is somewhat rare among the typical ratio questions that you'll see on Test Day. THOSE questions can normally be solved by doing Algebra, TESTing THE ANSWERS or by doing 'brute force' Arithmetic.

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Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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29 Jan 2015, 00:38
4

............................... Milk ............... Water ....................... Total

Initial ...................... 24 .................... 16 .............................. 40

20 Lts mix. taken out 24-12 ............... 16-8 ........................... 40-20

20 Lts milk added..... 12+20 ................ 8 .............................. 40

20 Lts mix. taken out 32-16 ............... 8-4 ........................... 40-20

20 Lts water added..... 16 ................ 4+20 .............................. 40

New ratio = 16:24 = 2:3
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Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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29 Jan 2015, 00:53
2
maxk297 wrote:
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.

C: 2:3

I took the long route.. i would like to solve this algebraically.. I am pondering over that now...

Actually, there is a formula for such replacement questions....

$$Final_Concentration = Initial_Concentration * (1 - \frac{Replace}{Total})^{Number_of_replacements}$$
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Posts: 5938
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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29 Jan 2015, 01:05
PareshGmat wrote:
maxk297 wrote:
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.

C: 2:3

I took the long route.. i would like to solve this algebraically.. I am pondering over that now...

Actually, there is a formula for such replacement questions....

$$Final_Concentration = Initial_Concentration * (1 - \frac{Replace}{Total})^{Number_of_replacements}$$

Although nopt tried the formula on this Q, I think the formulae will stand if same item is replaced or added.. here u have two different items being added on both occassions
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Joined: 02 Sep 2009
Posts: 46297
Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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02 Feb 2015, 03:29
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

In this word problem, the key to success is staying organized and following the changes in value. The mixture begins with a 3:2 ratio of milk to water, so out of 40 liters you have:

24 milk, 16 water

The first change is that the milkman removes half of that mixture, so cut those totals in half:

12 milk, 8 water

Then he adds 20 liters of milk, so add 20 to the milk total, making the running tally:

32 milk, 8 water

The next step is to take out half of that mixture, so you'll cut those totals in half:

16 milk, 4 water

And then add 20 liters of water to get the final mixture:

16 milk, 24 water

Since that's the final mixture, take that as a ratio. 16 and 24 are each multiples of 8, so you have (2 * 8) milk and (3 * 8) water, leading to a ratio of 2:3.
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Re: A dishonest milkman sells a 40 liter mixture of milk and water that co [#permalink]

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04 Oct 2017, 16:39
Bunuel wrote:
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?

A. 2:5
B. 3:5
C. 2:3
D. 3:2
E. 5:3

The original mixture has a ratio of milk to water = 3x : 2x, and thus:

40 = 5x

x = 8

So, originally there were 3(8) = 24 liters of milk and 2(8) = 16 liters of water.

Since 20 liters of the mixture (i.e., half of the mixture) are removed, half of the milk (12 liters) and half of the water (8 liters) are removed. Thus, after 20 liters are removed, there are:

12 liters of milk and 8 liters of water in the mixture.

Since 20 liters of milk are added back in, we now have:

32 liters of milk and 8 liters of water in the mixture.

Since another 20 liters of the mixture (i.e., half of the mixture) are removed, half of the milk (16 liters) and half of the water (4 liters) are removed. Thus, after 20 liters are removed, there are:

16 liters of milk and 4 liters of water in the mixture.

Since 20 liters of water are added back in, we now have:

16 liters of milk and 24 liters of water in the mixture.

Thus, the final ratio of milk to water is 16/24 = 2/3.

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Re: A dishonest milkman sells a 40 liter mixture of milk and water that co   [#permalink] 04 Oct 2017, 16:39
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