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In 70 litres of a mixture of milk and water, the quantity of water is

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TomB
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In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   24 Jan 2012, 14:40
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In 70 litres of a mixture of milk and water, the quantity of water is 10%. How much water should be added so that new mixture may contain 25%.

A. 10
B. 11
C. 12
D. 13
E. 14
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E
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KarishmaB
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In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   Updated on: 08 Oct 2022, 03:38
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TomB wrote:
In 70 liters of a mixture of milk and water ,the quantity of water is 10%. how much water should be added so that new mixture may 25% water.
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14

can it solve through chemical mixture strategy in mgmat guide


Once you get used to this method of solving, you will pretty much be solving this question orally. See if this makes sense:

Solution 1 has 10% water.
Solution 2 has 100% water. (You are mixing solution 1 with pure water.)
Mixture should have 25% water.
w1/w2 = (100 – 25)/(25 – 10) = 75/15 = 5/1
So volume of solution 1 : volume of water = 5:1
Solution 1 is 70 litres, so 14 litres of water must be added.

Originally posted by KarishmaB on 25 Jan 2012, 04:36.
Last edited by KarishmaB on 08 Oct 2022, 03:38, edited 1 time in total.
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   24 Jan 2012, 14:51
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TomB wrote:
In 70 liters of a mixture of milk and water ,the quantity of water is 10%. how much water should be added so that new mixture may 25% water.
Show Spoiler
14

can it solve through chemical mixture strategy in mgmat guide


Please post answer choices for PS problems. Also make sure you don't reword the questions you post.

As for the question:
There are 10% of water in 70L --> there are 7L of waters;
After x liters of water is added amount of water becomes (7+x) liters, which on the other hand is 1/4th (25%) of new (70+x) liters of mixture: 7+x=1/4*(70+x) --> 28+4x=70+x --> x=14.

Hope it's clear.
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   25 Jan 2012, 02:16
70 = 0,1W + 0,9M
Water = 7 Liter

New1: Add x-Liter water to increase W% from 10% to 25%
New2:
7+x = (70+x)1/4
-42/4 = -3/4x
14 = x

You need to add 14 Liter of Water to get a total of 21 Liter of Water in 84Liter of mixture
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   25 Jan 2012, 09:15
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my way
now water is 7/70
it will be (7+X)/(70+X) and it shoud =1/4.
solve and get the answer
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   25 Jan 2012, 11:43
first the amount of water was 70*10%=7

(7+x)/(70+x)=1/4
x=14
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   26 Jan 2012, 06:25
In 70 ltr solution we have 63 ltr of milk and 7 ltr of water
now we are adding water but the amount of milk remains constant so (70+x)*75/100 = 63 where x is the amount of water added
on solving x=14
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   28 Feb 2012, 18:23
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I draw the solution for you (attached). It might help you understand it a bit easier.
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mixture.png
mixture.png [ 25.98 KiB | Viewed 27742 times ]

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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   29 Feb 2012, 13:18
(7+x)/(70+x)=1/4
Solve for x; x=14
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   15 Apr 2012, 21:44
Karishma,

I found your post on mixtures very useful. I am stuck in the above problem. Please help
I solved w1/w2 to be
(90-25)/(25-10) = 65/15.

Can you please explain how you got 75/15?
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   17 Apr 2012, 11:44
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ENAFEX wrote:
Karishma,

I found your post on mixtures very useful. I am stuck in the above problem. Please help
I solved w1/w2 to be
(90-25)/(25-10) = 65/15.

Can you please explain how you got 75/15?


The two mixtures are: a 10% water solution, only water (which is 100% water)
We combine them to get 25% water solution.
Therefore, it is actually (100 - 25)/(25 - 10) and not (90 - 25)/(25 - 10)
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   15 Dec 2014, 05:27
VeritasPrepKarishma, How can we come to know which problems can be solved using the weighted averages formula..Is it applicable to all mixture problems?Or specific ones?
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In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   Updated on: 11 Oct 2022, 00:24
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Ralphcuisak wrote:
VeritasPrepKarishma, How can we come to know which problems can be solved using the weighted averages formula..Is it applicable to all mixture problems?Or specific ones?


For most mixture problems, weighted average formula is quite convenient. Whenever you add two things and consider the final solution or have the final solution and split it into two, weighted averages formula is relevant.

Originally posted by KarishmaB on 15 Dec 2014, 19:59.
Last edited by KarishmaB on 11 Oct 2022, 00:24, edited 1 time in total.
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   16 Dec 2014, 01:14
Thank you for the response Karishma..Will look into the article and implement it for mixture problems..
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   24 Apr 2020, 07:17
TomB wrote:
In 70 litres of a mixture of milk and water, the quantity of water is 10%. How much water should be added so that new mixture may contain 25%.

A. 10
B. 11
C. 12
D. 13
E. 14


90% of milk means 63 litres will remain the same in the final mix. 63 is the 75% of?

63 * 100/75 = 63 * 4/3 = 21 * 4 = 84

Si the final mix will have 84 litres.

84 - 70 = 14

We need to add 14 litres of water

Posted from my mobile device
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   24 Apr 2020, 20:29
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TomB wrote:
In 70 litres of a mixture of milk and water, the quantity of water is 10%. How much water should be added so that new mixture may contain 25%.

A. 10
B. 11
C. 12
D. 13
E. 14


I would use Options.

M=63 W=7

Lets add 13 litres of W. We get 20/83. Nope.

Let's add 14 litres of W. We get 21/84=25%. Answer E. (8.4+8.4+4.2=21)
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   27 May 2020, 10:34
Answer: Option E

This can be solved quickly using the Weighted Average

\(70 / W = (100 - 25) / (25 - 20)\)

=> \(W = (70 * 15) / 75 = 14 (E)\)
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   14 Sep 2020, 09:57
Can we use Alligation for this question?
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   20 Oct 2020, 14:08
7+X / 70+X = 1/4
70+x = 28 + 4x
42 = 3x
14 = x

Answer is E.
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Re: In 70 litres of a mixture of milk and water, the quantity of water is [#permalink] In 70 litres of a mixture of milk and water, the quantity of water is   03 Dec 2022, 11:12
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