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?

Correct answer marked below

853 : 827

Correct

53 : 48

53 : 27

53 : 25

53 : 23

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Explanation

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Official Explanation

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Let us concentrate the quantity of A in the mixture.

1) First container ratio 3:2

The proportion of total volume from this container is

\frac{1}{1+2+3}

\frac{1}{6}

.

So the quantity of A from first container =

\frac{3}{5}*\frac{1}{6}=\frac{1}{10}

2) Second container ratio 2:5

The proportion of total volume from this container is

\frac{2}{6}

.

So the quantity of A from second container =

\frac{2}{7}*\frac{2}{6}=\frac{2}{21}

…

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.