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Liquids A and B are in the ratio 2:1 in the first container and 1:2 in 26 Oct 2020, 09:17
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84% (00:55) correct 16% (01:49) wrong based on 57 sessions

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Liquids A and B are in the ratio 2:1 in the first container and 1:2 in the second container. In what ratio should the contents of the two containers be mixed to obtain a mixture of A and B in the ratio 1:1?

A. 4:1
B. 3:1
C. 2:1
D. 1:1
E. 1:2
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D
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Liquids A and B are in the ratio 2:1 in the first container and 1:2 in 26 Oct 2020, 09:38
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Not sure if my thought process is correct. But here is what I believe

In the first container we have 2a unita of liquid A and b units of liquid B.

In the second container we have a units of liquid A and 2b units of liquid b.

Now we need to mix the two to get A:B = 1:1.

Total A = 2a (#1 container) + a (#2 container) --> 3a

Total B = b (#1 container) + 3b (#2 container) --> 3b

A:B = 1:1

3a = 3b
a = b

(D)

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Liquids A and B are in the ratio 2:1 in the first container and 1:2 in 28 Oct 2020, 01:44
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Hoozan
Not sure if my thought process is correct. But here is what I believe

In the first container we have 2a unita of liquid A and b units of liquid B.

In the second container we have a units of liquid A and 2b units of liquid b.

Now we need to mix the two to get A:B = 1:1.

Total A = 2a (#1 container) + a (#2 container) --> 3a

Total B = b (#1 container) + 3b (#2 container) --> 3b

A:B = 1:1

3a = 3b
a = b

(D)

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Bunuel could you throw some light on the solution? I am don't feel 100% confident with my thought process
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Liquids A and B are in the ratio 2:1 in the first container and 1:2 in 28 Oct 2020, 05:44
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Same here, could you elaborate a bit more on the thought process and the why? I lucked out on this question, but not sure why
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Liquids A and B are in the ratio 2:1 in the first container and 1:2 in 07 Nov 2020, 10:16
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rohanbnj
Same here, could you elaborate a bit more on the thought process and the why? I lucked out on this question, but not sure why
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I think Hoozan did a great job getting to why the total quantity of the containers are equal and of opposing parts, but I think that intuition can to be expounded upon.

Let me try to explain the best I can.

Taking a look at the following containers:

1) Liquid \(A_{1}:B_{1}\) ==> 1:2. This means the total volume of the can is \(3x = 1x + 2x\)
2) Liquid \(A_{2}:B_{2}\) ==> 2:1. This means the total volume of the can is \(3y = 2y + 1y\)

The goal of this problem is to see what portion of each can needs to be mixed for A to Equal B.

i.e. Figure out \(3x:3y\)

We can set this equation up this way because we do not know the exact quantities of liquid respective to each container (e.g. x vs y), but we know that it is dispersed in parts within each container in a formulaic way (e.g. 1:2).

Now we are trying to combine the mixtures to have equal parts of A to B.
This means we can set up a system of equations where \(A_{1} + A_{2} = B_{1} + B_{2} \) (same as saying 1:1).

\(x + 2y = 2x + y\) which just gives us \(y = x\).

This means that the total volume of each can (\(3x\) and \(3y\)) must be equal to each other IF we set the total parts of A equal to the total parts of B.

\(3x:3y\) is \(1:1\).
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