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

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Senior Manager
Joined: 28 Jun 2015
Posts: 299
Concentration: Finance
GPA: 3.5
A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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17 Jul 2017, 21:20
11
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Difficulty:

95% (hard)

Question Stats:

35% (03:04) correct 65% (02:44) wrong based on 51 sessions

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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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Manager
Joined: 14 Oct 2015
Posts: 227
A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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17 Jul 2017, 22:38
1
KUDOS
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,

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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Intern
Joined: 13 May 2017
Posts: 24
Re: A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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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,

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.
Manager
Joined: 14 Oct 2015
Posts: 227
Re: A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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18 Jul 2017, 01:46
1
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,

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.
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Senior Manager
Joined: 02 Apr 2014
Posts: 354
Re: A 10-liter milk jug contains milk and water in the ratio 7:3 [#permalink]

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13 Nov 2017, 13:03
1
This post was
BOOKMARKED
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,

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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