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A milkman ordered his assistant to first remove 3 litres out of the 8

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A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 19 Dec 2018, 09:55
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Question Stats:

58% (02:49) correct 42% (02:40) wrong based on 111 sessions

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A milkman ordered his assistant to first remove 3 liters out of the 8 liters of a solution of milk and water and then add 3 liters of water to it. Thinking that it would not make any difference, the lab assistant first added 3 liters of water and then removed 3 liters of the solution. Find the ratio of the expected concentration of the milk to the actual concentration of the milk.

A 1:1
B 21:52
C 55:64
D 3:4
E 6:11
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Re: A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 19 Dec 2018, 10:56
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Imagine 8L of the solution includes 4L water and 4L milk.
reduce 3L of the solution, then has 2.5L water and 2.5L milk
Then add 3L of water, now in the bottle, there are 5.5L water and 2.5L milk, so the expected concentration of the milk is 5/16

The way that the assistant did makes the milk in the bottle before remove is still 4L, and the water is 7L. No matter it's removed or not,the concentration of the milk in the bottle is 4/11

So, answer: (5/16)/(4/11)=C
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Re: A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 28 Dec 2018, 14:11
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Hi, chetan2u, Bunuel, please help me out with this. I don't understand a part of this explanation. The question doesn't explicitly state the ratio of milk to water in the original solution. Are we just goingbto assume that it's 1:1 as stated in the above explanation or am I missing something stated in the question that implies the ratio in the explanation. Happy Holidays btw.

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A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 28 Dec 2018, 19:35
Kem12 wrote:
Hi, chetan2u, Bunuel, please help me out with this. I don't understand a part of this explanation. The question doesn't explicitly state the ratio of milk to water in the original solution. Are we just goingbto assume that it's 1:1 as stated in the above explanation or am I missing something stated in the question that implies the ratio in the explanation. Happy Holidays btw.

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Hi..

It will not make a difference what you take except when you take initial milk to be 0.
Because then the concentration will be 0 in both times.

Let the entire solution be water, so 8 litres of water..
(I) expected milk 5...after taking out 3 litres of milk and replaced with water.
(II) actual ..After addition of 3 litres of water total milk is 8 out of 11 litres of solution. therefore if you take out 3 litres, milk taken out 3*8/11=24/11..
Milk left is 8-(24/11)=64/11.

Ratio of concentration.. (5)/8: (64/11)/8 =5:64/11 =55:64
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A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 29 Dec 2018, 02:25
Hi chetan2u, thanks for the explanation. Much clearer now.

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Re: A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 30 Dec 2018, 11:25
Hi chetan2u,

I didn't get some part of your reply, which I've mentioned below. Can you please explain it.

(I) expected milk 5.
(II) actual ..
Total milk 8/11..

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Re: A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 02 Jan 2019, 20:53
yoliwu wrote:
Imagine 8L of the solution includes 4L water and 4L milk.
reduce 3L of the solution, then has 2.5L water and 2.5L milk
Then add 3L of water, now in the bottle, there are 5.5L water and 2.5L milk, so the expected concentration of the milk is 5/16

The way that the assistant did makes the milk in the bottle before remove is still 4L, and the water is 7L. No matter it's removed or not,the concentration of the milk in the bottle is 4/11

So, answer: (5/16)/(4/11)=C


Hello!

Could someone explain to me where does the 5/16 come from?

Regards!
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Re: A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 09 Jan 2019, 03:25
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jfranciscocuencag wrote:
yoliwu wrote:
Imagine 8L of the solution includes 4L water and 4L milk.
reduce 3L of the solution, then has 2.5L water and 2.5L milk
Then add 3L of water, now in the bottle, there are 5.5L water and 2.5L milk, so the expected concentration of the milk is 5/16

The way that the assistant did makes the milk in the bottle before remove is still 4L, and the water is 7L. No matter it's removed or not,the concentration of the milk in the bottle is 4/11

So, answer: (5/16)/(4/11)=C


Hello!

Could someone explain to me where does the 5/16 come from?

Regards!



You don’t have to follow the solution provided.
First, it is about concentration ratio
It is up to you to define the initiative ratio.
So let us make it 8L of milk instead.

You reduce 3L milk and add 3L water
Concentration ratio: 5/8
You add 3L water and reduce 3L of the mixture
Concentration ratio :8/11

5/8:8/11
55/88:64/88
55:64

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Re: A milkman ordered his assistant to first remove 3 litres out of the 8  [#permalink]

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New post 16 Jan 2019, 23:03
@khorwie "You add 3L water and reduce 3L of the mixture
Concentration ratio :8/11" if we remove 3 L of the mixture the remaining mixture should be 8L not 11 L right? so how is the ratio coming out to be 8/11?
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Re: A milkman ordered his assistant to first remove 3 litres out of the 8   [#permalink] 16 Jan 2019, 23:03
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