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A 10-liter milk jug contains milk and water in the ratio 7:3

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A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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New post 17 Jul 2017, 21:20
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Question Stats:

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A 10-liter contents of a milk and water mixture are in the ratio 7:3. The mixture is removed and replaced with water to bring down the concentration of milk by 10%. The amount, in litres, of water that needs to be added to the resulting mixture in order to reduce the concentration of milk to 50% is

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
[Reveal] Spoiler: OA

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A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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New post 17 Jul 2017, 22:38
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TimeTraveller wrote:
A 10-liter contents of a milk and water mixture are in the ratio 7:3. The mixture is removed and replaced with water to bring down the concentration of milk by 10%. The amount, in litres, of water that needs to be added to the resulting mixture in order to reduce the concentration of milk to 50% is

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16


It should be D.

When we replace 10 litres of mixture from total with water, here is what we are doing.

Removing 7 litres milk,
Aemoving 3 litres water,
Adding 10 litres water

If removing 7 litres of milk reduces %age by 10 and adding 7 litres of water increases its %age in solution by 10,

7L = 10%
7 x 10 = 70 litres solution.

Now after reducing, we are left with 60% milk and 40% water.

\(Milk = 70*\frac{6}{10}\) = 42 L

\(Water = 70 - 42 = 28\)

To make it a 50/50 solution, we need to add 42-28 = 14 Litres of water.
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Re: A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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New post 17 Jul 2017, 22:58
jedit wrote:
TimeTraveller wrote:
A 10-liter contents of a milk and water mixture are in the ratio 7:3. The mixture is removed and replaced with water to bring down the concentration of milk by 10%. The amount, in litres, of water that needs to be added to the resulting mixture in order to reduce the concentration of milk to 50% is

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16


It should be D.

When we replace 10 litres of mixture from total with water, here is what we are doing.

Removing 7 litres milk,
Aemoving 3 litres water,
Adding 10 litres water

If removing 7 litres of milk reduces %age by 10 and adding 7 litres of water increases its %age in solution by 10,

7L = 10%
7 x 10 = 70 litres solution.

Now after reducing, we are left with 60% milk and 40% water.

\(Milk = 70*\frac{6}{10}\) = 42 L

\(Water = 70 - 42 = 28\)

To make it a 50/50 solution, we need to add 42-28 = 14 Litres of water.



out of 10 liters if we remove 7 + 3 L we will not be left with anything :-(. Please help me understand how you arrived at 70L solution.
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Re: A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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New post 18 Jul 2017, 01:46
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KUDOS
KanakGarg wrote:
jedit wrote:
TimeTraveller wrote:
A 10-liter contents of a milk and water mixture are in the ratio 7:3. The mixture is removed and replaced with water to bring down the concentration of milk by 10%. The amount, in litres, of water that needs to be added to the resulting mixture in order to reduce the concentration of milk to 50% is

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16


It should be D.

When we replace 10 litres of mixture from total with water, here is what we are doing.

Removing 7 litres milk,
Aemoving 3 litres water,
Adding 10 litres water

If removing 7 litres of milk reduces %age by 10 and adding 7 litres of water increases its %age in solution by 10,

7L = 10%
7 x 10 = 70 litres solution.

Now after reducing, we are left with 60% milk and 40% water.

\(Milk = 70*\frac{6}{10}\) = 42 L

\(Water = 70 - 42 = 28\)

To make it a 50/50 solution, we need to add 42-28 = 14 Litres of water.



out of 10 liters if we remove 7 + 3 L we will not be left with anything :-(. Please help me understand how you arrived at 70L solution.


This is word trickery. Read this : A 10-liter contents of a milk and water mixture are in the ratio 7:3

This means ratio of solution is 7:3 but A 10 liter content means we are selecting a 10 liter part of the whole solution, that we are removing. Kudos if it helps.
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Joined: 02 Apr 2014
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Re: A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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New post 13 Nov 2017, 13:03
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KanakGarg wrote:
jedit wrote:
TimeTraveller wrote:
A 10-liter contents of a milk and water mixture are in the ratio 7:3. The mixture is removed and replaced with water to bring down the concentration of milk by 10%. The amount, in litres, of water that needs to be added to the resulting mixture in order to reduce the concentration of milk to 50% is

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16


It should be D.

When we replace 10 litres of mixture from total with water, here is what we are doing.

Removing 7 litres milk,
Aemoving 3 litres water,
Adding 10 litres water

If removing 7 litres of milk reduces %age by 10 and adding 7 litres of water increases its %age in solution by 10,

7L = 10%
7 x 10 = 70 litres solution.

Now after reducing, we are left with 60% milk and 40% water.

\(Milk = 70*\frac{6}{10}\) = 42 L

\(Water = 70 - 42 = 28\)

To make it a 50/50 solution, we need to add 42-28 = 14 Litres of water.



out of 10 liters if we remove 7 + 3 L we will not be left with anything :-(. Please help me understand how you arrived at 70L solution.


I think poor wording question.
Read the question as -> there is certain litres of mixture of milk and water in ratio 7:3. Out of which, 10 litres is removed and replaced with water to bring down concentration of milk by 10% ...

Then you will be able to solve it
Re: A 10-liter milk jug contains milk and water in the ratio 7:3   [#permalink] 13 Nov 2017, 13:03
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A 10-liter milk jug contains milk and water in the ratio 7:3

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