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Quantitative Aptitude

Mixture & Alligations

The ratio of ...

Question

The ratio of the volume of three buckets is 3:4:5. buckets contains the mixture of water and alcohol. if the mixture contains water and alcohol in the ratio 1:4,1:3 and 2:5 respectively then find the ratio of water and alcohol when the mixture in all containers are poured in fourth container.

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Solution

Let the volumes be 3x, 4x, and 5x
$3 x = 1 : 4 (W a t e r) \frac{3 x}{1 + 4} \times 1 = \frac{3 x}{5} A l c o h o l \frac{3 x}{1 + 4} \times 4 = \frac{12 x}{5}$
$4 x = 1 : 3 (W a t e r) \frac{4 x}{1 + 3} \times 1 = \frac{4 x}{4} = x A l c o h o l \frac{4 x}{1 + 3} \times 3 = \frac{12 x}{4} = 3 x$
$5 x = 2 : 5 (W a t e r) \frac{5 x}{7} \times 2 = \frac{10 x}{7} A l c o h o l \frac{5 x}{7} \times 5 = \frac{25}{7} x$
Total water
$\frac{3 x}{5} + x + \frac{10 x}{7} = \frac{21 x + 35 x + 50 x}{35} = \frac{106 x}{35}$
Total Alcohol
$\frac{12 x}{5} + 3 x + \frac{25 x}{7} = \frac{84 x + 105 x + 125 x}{35} = \frac{314 x}{35}$
Overall ratio
$= \frac{\frac{106 x}{35}}{\frac{314 x}{35}} = \frac{106}{314} = \frac{53}{157}$

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