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# If after 200 grams of water were added to the 24% solution

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Director
Joined: 17 Dec 2012
Posts: 619
Location: India
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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10 Jun 2017, 03:16
bibha wrote:
If after 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?

A. 180 grams
B. 220 grams
C. 250 grams
D. 350 grams
E. 400 grams

1. Let the quantity of the solution be x.
2. (Quantity of 24% solution)* (Strength of the solution )+ ( Quantity of water added)*(strength of water)/ (total quantity)=strength of the resultant solution
3. (x*0.24 ) + (200*0)/ (x+200) =16/100
x=400
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Srinivasan Vaidyaraman
Magical Logicians

Holistic and Holy Approach
Intern
Joined: 18 May 2015
Posts: 21
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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12 Jun 2017, 16:23
Is there a standard way to attack mixture problems? There are so many different ways of solving the problem its confusing.
VP
Joined: 07 Dec 2014
Posts: 1242
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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12 Jun 2017, 18:13
bibha wrote:
If after 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?

A. 180 grams
B. 220 grams
C. 250 grams
D. 350 grams
E. 400 grams

let x=grams of 24% solution used
.76x+200=.84(x+200)
x=400 grams
E
Director
Joined: 17 Dec 2012
Posts: 619
Location: India
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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12 Jun 2017, 18:25
oa7 wrote:
Is there a standard way to attack mixture problems? There are so many different ways of solving the problem its confusing.

You are right. Most of the problems in a topic can be solved by using a common approach. I try to use such an approach. So even if for some problems there may be quicker solutions than a standard solution, trying to think of such quick solutions take time. In a standard approach, you automatically apply the same steps for seemingly different types of problems.
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Srinivasan Vaidyaraman
Magical Logicians

Holistic and Holy Approach
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10240
Location: Pune, India
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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14 Jun 2017, 03:11
1
oa7 wrote:
Is there a standard way to attack mixture problems? There are so many different ways of solving the problem its confusing.

Usually, weighted averages will help.

Check these three posts:

https://www.veritasprep.com/blog/2011/0 ... -averages/
https://www.veritasprep.com/blog/2011/0 ... -mixtures/
https://www.veritasprep.com/blog/2012/0 ... -mixtures/

They will help you sort out most of the mixture problems.
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Karishma
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Affiliations: Target Test Prep
Joined: 14 Oct 2015
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Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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20 Jun 2017, 06:33
bibha wrote:
If after 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?

A. 180 grams
B. 220 grams
C. 250 grams
D. 350 grams
E. 400 grams

Since 1/3 of 24 is 8, we know that after 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased to 16%. We can let the original amount of solution = x, and thus the original amount of alcohol = 0.24x. We can create the following equation and solve for x:

0.24x/(x + 200) = 0.16

0.24x = 0.16(x + 200)

0.24x = 0.16x + 32

0.08x = 32

x = 32/0.08 = 3200/8 = 400

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Intern
Joined: 19 Sep 2018
Posts: 3
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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22 Sep 2018, 21:29
Simple Equation:
.24x/(.76x+200)=16/84
=> x=400 grams
Intern
Joined: 31 Mar 2017
Posts: 8
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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13 Dec 2018, 20:01
24% of x = (24%*2/3) of (x+200)
Solving, x = 400

Posted from my mobile device
VP
Joined: 24 Nov 2016
Posts: 1349
Location: United States
Re: If after 200 grams of water were added to the 24% solution  [#permalink]

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24 Jan 2020, 09:12
bibha wrote:
If after 200 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?

A. 180 grams
B. 220 grams
C. 250 grams
D. 350 grams
E. 400 grams

alcohol_after=alcohol_before(volume_initial/volume_final)
0.24*2/3=0.24(x/x+200)
0.16x+200(0.16)=0.24x
0.08x=200(0.16)
x=200*2=400

Ans (E)
Re: If after 200 grams of water were added to the 24% solution   [#permalink] 24 Jan 2020, 09:12

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# If after 200 grams of water were added to the 24% solution

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