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

BongBideshini · Answer

heavy calculation. It took me around 4 mins.

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

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

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