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

Question

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 %

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

firas92 · Accepted Answer

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%

Answer is (D)

Anulitha · Answer

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%

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%.

Posted from my mobile device

Anulitha · Answer

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

Anulitha · Answer

Posted from my mobile device

Anulitha · Answer

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

Posted from my mobile device

ajaykv · Answer

VeritasKarishma  /  Bunuel  can you please post a solution for this

KarishmaB · Answer

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%

Answer (D)

lacktutor · Answer

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 %

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  %

Answer (D).

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards