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

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Re: Three containers are filled with a mixture of A and B each. The volume [#permalink]
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Bunuel wrote:
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

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
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Three containers are filled with a mixture of A and B each. The volume [#permalink]
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Quote:
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?

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
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Re: Three containers are filled with a mixture of A and B each. The volume [#permalink]
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
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Re: Three containers are filled with a mixture of A and B each. The volume [#permalink]
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