Question

Two vessels contain a mixture of spirit and water. In the first vessel the ratio of spirit to water is 8:3 and in the second vessel, the ratio is 5:1. A 35 litre cask is filled from these vessels so as to contain a mixture of spirit and water in the ratio of 4:1. How many litres are taken from the first vessel?

• A. 11 litres
• B. 22 litres
• C. 16.5 litres
• D. 17.5 litres

Answer 1

The correct option is A 11 litres

Concentration of spirit in first vessel = $\frac{8}{11}=\frac{48}{66}$
Concentration of spirit in second vessel = $\frac{5}{6}=\frac{55}{66}$
Concentration of spirit in the final mixture = $\frac{4}{5}=\frac{52.8}{66}$
Hence we obtain the alligation as:

Ratio of liquids from first vessel to that from second = $\frac{2.2}{4.8}$
$\therefore$ Litres taken from the first vessel = $\frac{2.2}{7}\times 35=11litres$


Alternatively:
Fit the conditions of the problem as if there are 11 litres in the first vessel, there would be 8 litres of spirit. Also, it means that we would be taking 24 litres from the second vessel out of which there would be 20 litres of spirit. Thus, the total spirit would be 28 out of 35 litres giving us 7 litres of water.