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

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Bunuel
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Three containers are filled with a mixture of A and B each. The volume [#permalink] New post   05 Mar 2021, 10:00
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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
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chetan2u
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Re: Three containers are filled with a mixture of A and B each. The volume [#permalink] New post   05 Mar 2021, 20:25
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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 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

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Re: Three containers are filled with a mixture of A and B each. The volume [#permalink] New post   23 Mar 2021, 05:08
please elaborate in a simpler way
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Re: Three containers are filled with a mixture of A and B each. The volume [#permalink] New post   23 Mar 2021, 05:50
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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

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Three containers are filled with a mixture of A and B each. The volume [#permalink] New post   18 Dec 2021, 04:52
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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] New post   13 Feb 2023, 11:24
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Re: Three containers are filled with a mixture of A and B each. The volume [#permalink]
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