GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Jul 2020, 12:08

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A solution of milk and water having 20% milk is mixed with another sol

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65062
A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

31 Dec 2019, 02:22
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:39) correct 42% (02:48) wrong based on 67 sessions

### HideShow timer Statistics

A solution of milk and water having 20% milk is mixed with another solution having 50% milk in the ratio 2 : 5. If 21 lts of this mixture is taken and mixed with 9 lts of another milk and water solution having 80% milk, find the percentage of milk in the final mixture.

A. 43 %
B. 47 %
C. 50 %
D. 53 %
E. 57 %

_________________
Intern
Joined: 08 Dec 2019
Posts: 11
Re: A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

01 Jan 2020, 00:49
Consider total solution (milk and water) in first and second solution as 100L. Both of them mixed in 2:5 ratio.
By principle of alligation (consider ratio of milk)
2/7 = (x-1/5)/(1/2-x)
Solve for x (x is milk ratio in final mixture), we get x=4/15 and
Therefore water = 11/15.
Therefore Milk:water in final solution is 4:11

Then 21 litres of this solution is taken. Concentration of milk in 21 litres = 27% [(4/15)*21=28/5. Therefore what percentage of 21 will be 28/5? Solve for that and you get 26.6% rounded off to 27%.]

Use formula:
Conc of milk*vol of milk added + conc of milk*vol of milk existing =
Conc of milk*total vol

27%*21+80*9=x*30
Solve for x, we get 43%.

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
Director
Joined: 16 Jan 2019
Posts: 652
Location: India
Concentration: General Management
WE: Sales (Other)
Re: A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

01 Jan 2020, 01:55
1
2
Solution A = 20% milk, 80% water
Solution B = 50% milk, 50% water
Solution C = 80% milk, 20% water

Volume of A = 2/7*21 = 6 liters (so 6*0.2 = 1.2 liters of milk)
Volume of B = 5/7*21 = 15 liters (so 15*0.5 = 7.5 liters of milk)
Volume of C = 9 liters (so 9*0.8 = 7.2 liters of milk)

Total Volume of mixture = 6+15+9 = 30
Total Volume of milk = 1.2+7.5+7.2 = 15.9

Percentage of milk in final mix = 15.9/30 = 5.3/10 = 53%

Intern
Joined: 08 Dec 2019
Posts: 11
Re: A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

04 Jan 2020, 21:46
Can we solve this with rule of alligation? I see the error in my solution. But, if two solutions are mixed in the ratio of 2:5 can we not apply the below?
2/5=(50-x)/(x-30)
Solve for x. X=30%
Then use formula of concentration
21*30%+9*80%=30*y%
Solve for y. I got the wrong answer. However, I do not understand why we can't use this.

Posted from my mobile device
Intern
Joined: 08 Dec 2019
Posts: 11
Re: A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

04 Jan 2020, 21:46
firas92 wrote:
Solution A = 20% milk, 80% water
Solution B = 50% milk, 50% water
Solution C = 80% milk, 20% water

Volume of A = 2/7*21 = 6 liters (so 6*0.2 = 1.2 liters of milk)
Volume of B = 5/7*21 = 15 liters (so 15*0.5 = 7.5 liters of milk)
Volume of C = 9 liters (so 9*0.8 = 7.2 liters of milk)

Total Volume of mixture = 6+15+9 = 30
Total Volume of milk = 1.2+7.5+7.2 = 15.9

Percentage of milk in final mix = 15.9/30 = 5.3/10 = 53%

Quote:
Can we solve this with rule of alligation? I see the error in my solution. But, if two solutions are mixed in the ratio of 2:5 can we not apply the below?
2/5=(50-x)/(x-30)
Solve for x. X=30%
Then use formula of concentration
21*30%+9*80%=30*y%
Solve for y. I got the wrong answer. However, I do not understand why we can't use this.

Posted from my mobile device
Intern
Joined: 08 Dec 2019
Posts: 11
Re: A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

04 Jan 2020, 21:52
firas92 wrote:
Solution A = 20% milk, 80% water
Solution B = 50% milk, 50% water
Solution C = 80% milk, 20% water

Volume of A = 2/7*21 = 6 liters (so 6*0.2 = 1.2 liters of milk)
Volume of B = 5/7*21 = 15 liters (so 15*0.5 = 7.5 liters of milk)
Volume of C = 9 liters (so 9*0.8 = 7.2 liters of milk)

Total Volume of mixture = 6+15+9 = 30
Total Volume of milk = 1.2+7.5+7.2 = 15.9

Percentage of milk in final mix = 15.9/30 = 5.3/10 = 53%

Nevermind I solved wrong for x. I got the right answer now.

Posted from my mobile device
Intern
Joined: 20 Apr 2016
Posts: 13
Re: A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

13 May 2020, 06:15
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India
Re: A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

14 May 2020, 20:33
1
1
Bunuel wrote:
A solution of milk and water having 20% milk is mixed with another solution having 50% milk in the ratio 2 : 5. If 21 lts of this mixture is taken and mixed with 9 lts of another milk and water solution having 80% milk, find the percentage of milk in the final mixture.

A. 43 %
B. 47 %
C. 50 %
D. 53 %
E. 57 %

Find we find the concentration of milk when 20% is mixed with 50%

Cavg = (C1*w1 + C2*w2)/ (w1 + w2)

Cavg`= (20*2 + 50*5) / (2+5) = (290/7) % = 41% milk in the mixture

Now we find the concentration fo milk when this resultant 41% (approx) is mixed with 80%

Cavg = (41*21 + 80*9) / (21 + 9) = 52.7%

_________________
Karishma
Veritas Prep GMAT Instructor

Director
Joined: 25 Jul 2018
Posts: 731
A solution of milk and water having 20% milk is mixed with another sol  [#permalink]

### Show Tags

15 May 2020, 22:02
A solution of milk and water having 20% milk is mixed with another solution having 50% milk in the ratio 2 : 5. If 21 lts of this mixture is taken and mixed with 9 lts of another milk and water solution having 80% milk, find the percentage of milk in the final mixture.

20% ----------x------50% (b liters)
(a liters)

$$\frac{a}{b} = \frac{2}{5}$$

---> $$\frac{50-x}{x-20 }= \frac{2}{5}$$

$$250 - 5x = 2x- 40$$

$$7x = 290$$

$$x = (\frac{290}{7})$$ %

The next equation will be:
$$21(\frac{290}{7}) + 9(80)= 30 y$$

$$y = \frac{(870+ 720) }{30} = \frac{1590}{30}= 53$$ %

A solution of milk and water having 20% milk is mixed with another sol   [#permalink] 15 May 2020, 22:02