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# A mixture of 40 liters of milk and water contains 10% water.

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Intern
Joined: 22 Oct 2010
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A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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Updated on: 04 Jul 2018, 06:18
2
10
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:40) correct 32% (01:38) wrong based on 149 sessions

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A mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

A. 4
B. 5
C. 6
D. 7
E. 8

Originally posted by munia123 on 27 Oct 2010, 12:57.
Last edited by abhimahna on 04 Jul 2018, 06:18, edited 1 time in total.
Edited the question and added OA
Math Expert
Joined: 02 Sep 2009
Posts: 57155
Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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27 Oct 2010, 17:44
1
5
munia123 wrote:

a mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

Provide answer choices for PS questions.

Let the amount of water to be added be $$x$$ liters.

We want the percentage of water to increase from 10% to 20% or percentage of non-water to decrease from 90% to 80%. Note that when we add $$x$$ liters of water the amount of non-water in mixture in liters remains the same, so:

$$0.9*40=0.8(40+x)$$ --> $$x=5$$.

Or, the amount of water after adding $$x$$ liters of water ($$0.2*(40+x)$$) should be equal to initial amount of water ($$0.1*40$$) plus the amount of water we add ($$x$$)

$$0.2*(40+x)=0.1*40+x$$ --> $$x=5$$.

Hope it helps.
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##### General Discussion
Intern
Joined: 19 Oct 2010
Posts: 3
Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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27 Oct 2010, 13:33
40 liters of mixture contains 4 liters of water (10%). So, it has 36 liters of milk.

if 36 liters <-> 80%,
100% <-> (36/80)x100 = 45 liters

So, the total water in the mixture should be 9 liters. Since there is already 4 liters in the mixture, 5 liters need to be added.
Manager
Joined: 25 Aug 2010
Posts: 61
Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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28 Oct 2010, 02:42
Bunuel wrote:
munia123 wrote:

a mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

Provide answer choices for PS questions.

Let the amount of water to be added be $$x$$ liters.

We want the percentage of water to increase from 10% to 20% or percentage of non-water to decrease from 90% to 80%. Note that when we add $$x$$ liters of water the amount of non-water in mixture in liters remains the same, so:

$$0.9*40=0.8(40+x)$$ --> $$x=5$$.

Or, the amount of water after adding $$x$$ liters of water ($$0.2*(40+x)$$) should be equal to initial amount of water ($$0.1*40$$) plus the amount of water we add ($$x$$)

$$0.2*(40+x)=0.1*40+x$$ --> $$x=5$$.

Hope it helps.

Hi Bunuel, i got the different ans.. let me know where i m wrong....

Problem again :
a mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

a mixture of 40 ltrs water + milk contains 10% of water so 4 ltrs are water rest 36 ltrs are milk.

if i want to make water 20% in the mixture
40*20% = (4+ x) here x is the water to be added to the mixture

so, i got x as 4

please suggest me if i gone wrong???

Math Expert
Joined: 02 Sep 2009
Posts: 57155
Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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28 Oct 2010, 02:56
vitamingmat wrote:
Bunuel wrote:
munia123 wrote:

a mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

Provide answer choices for PS questions.

Let the amount of water to be added be $$x$$ liters.

We want the percentage of water to increase from 10% to 20% or percentage of non-water to decrease from 90% to 80%. Note that when we add $$x$$ liters of water the amount of non-water in mixture in liters remains the same, so:

$$0.9*40=0.8(40+x)$$ --> $$x=5$$.

Or, the amount of water after adding $$x$$ liters of water ($$0.2*(40+x)$$) should be equal to initial amount of water ($$0.1*40$$) plus the amount of water we add ($$x$$)

$$0.2*(40+x)=0.1*40+x$$ --> $$x=5$$.

Hope it helps.

Hi Bunuel, i got the different ans.. let me know where i m wrong....

Problem again :
a mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

a mixture of 40 ltrs water + milk contains 10% of water so 4 ltrs are water rest 36 ltrs are milk.

if i want to make water 20% in the mixture
40*20% = (4+ x) here x is the water to be added to the mixture

so, i got x as 4

please suggest me if i gone wrong???

4+x liters of water is 20% of 40+x liters of mixture not 40.
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Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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28 Oct 2010, 04:06
thanks to bunuel and also thanks to that person who asked the question to bunnel ( i also thought that 40*20% = 40+x). now i have understood. thanks .
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Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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19 Apr 2014, 00:34
1
No need to complicate much.

4 ltr - Water
36 ltr - milk

Let X water be added then the new mixture must have 20% water

Then

4 + X = 20/100 (40+X)

X=5
Intern
Joined: 20 Sep 2014
Posts: 6
Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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27 Sep 2014, 00:40
munia123 wrote:

a mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

hi how would u solve this using the allegation method ?
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Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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29 Sep 2014, 01:18
1
Initial water = 4

Initial Solution = 40

Final water = 4+x

Final Solution = 40+x

$$\frac{4+x}{40+x} = \frac{20}{100} = \frac{1}{5}$$

x = 5

Answer = 5 (No OA for this question)
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Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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16 Apr 2017, 13:43
munia123 wrote:

a mixture of 40 liters of milk and water contains 10% water. how much water should be added to this so that water may be 20% in the new mixture?

.10*40+w=.20(40+w)
w=5 liters
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Re: A mixture of 40 liters of milk and water contains 10% water.  [#permalink]

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07 Aug 2019, 02:59
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Re: A mixture of 40 liters of milk and water contains 10% water.   [#permalink] 07 Aug 2019, 02:59
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