Three containers are filled with a mixture of A and B each. The volume

Question

Three containers are filled with a mixture of A and B each. The volume of the mixture in the three containers is in the ratio 1 : 2 : 3. The ratio of A and B in the three containers are 3 : 2, 2 : 5 and 5 : 3 respectively. The content of the containers are mixed in a single container of sufficient capacity. What is the ratio of A and B in the final mixture?

(A) 853 : 827
(B) 53 : 48
(C) 53 : 27
(D) 53 : 25
(E) 53 : 23

(A) 853 : 827
(B) 53 : 48
(C) 53 : 27
(D) 53 : 25
(E) 53 : 23

chetan2u · Accepted Answer

Let us concentrate the quantity of A in the mixture. 
1) 3:2
The ratio of this is  \frac{1}{1+2+3}  or  \frac{1}{6} .
So the quantity of A =  \frac{3}{5}*\frac{1}{6}=\frac{1}{10} 
2) 2:5
Similarly the quantity of A=  \frac{2}{7}*\frac{2}{6}=\frac{2}{21} 
3) 5:3
Similarly the quantity of A =  \frac{5}{8}*\frac{3}{6}=\frac{5}{16}

Quantity of A as a fraction of total =  \frac{1}{10}+\frac{2}{21}+\frac{5}{16}=\frac{21*16+2*10*16+5*21*10}{10*16*21}=\frac{1706}{3360}=\frac{853}{1680}

A:(A+B)=853:1680
So A:B=853-(1680-853)=853:827

A

nityakaul02 · Answer

please elaborate in a simpler way

chetan2u · Answer

Let us use some values for the volume of mix. 
The different ratios we are dealing with are 1:2:3, 3:2, 2:5 and 5:3.
Since we have to divide total mixture as per the ratios, let us take product of (1+2+3,3+2,2+5,5+3)=6*5*7*8=1680

So the total is 1680 l. 
1:2:3=280:560:840
1) First container
Total 280 in ratio of A:B as 3:2= 3*\frac{280}{3+2} :  2*\frac{280}{3+2} =168:112
2 ) Second container
Total 560 in ratio of A:B as 2:5= 2*\frac{560}{5+2} :  5*\frac{560}{5+2} =160:400
3 ) Third container
Total 420l in ratio of A:B as 5:3= 5*\frac{840}{3+5} :  3*\frac{840}{3+5} =525:315

So A = 168+160+525=853
B=1680-853=827

A

D33T · Answer

So... given that the three containers had volumes in the ratio 1: 2: 3, their total volume should come up to (1+2+3) =  6x. 
 
Total amount of A in the three containers = 3/5(x) + 2/7(2x) + 5/8(3x) =  \frac{853}{280} x
Total amount of B in the three containers = 2/5(x) + 5/7(2x) + 3/8(3x) =  \frac{827}{280} x

Ratio of A : B = 853 : 827

Kinshook · Answer

Given: Three containers are filled with a mixture of A and B each. The volume of the mixture in the three containers is in the ratio 1 : 2 : 3. The ratio of A and B in the three containers are 3 : 2, 2 : 5 and 5 : 3 respectively. The content of the containers are mixed in a single container of sufficient capacity.

Asked: What is the ratio of A and B in the final mixture?

Let the volume of mixture in the three containers be x, 2x & 3x respectively.

Container 1: 
Total = x
A = 3x/5
B = 2x/5

Container 2: 
Total = 2x
A = 4x/7
B = 10x/7

Container 3: 
Total = 3x
A = 15x/8
B = 9x/8

Final Single Container: 
Total = x + 2x + 3x = 6x
A = 3x/5 + 4x/7 + 15x/8 = 853x/280
A/Total = 853x/280*6x = 853/1680
B/Total = 1 - A/Total = 827/1680
A/B = 853/827
A:B = 853:827

IMO A

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.

Three containers are filled with a mixture of A and B each. The volume

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

Three containers are filled with a mixture of A and B each. The volume

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