Three containers whose volumes are in the ratio of 2 : 3 : 4 are full of mixture of spirit and water. In the 1st container the ratio of spirits and water is 4 : 1, in 2nd container the ratio is 11 : 4 and on the 3rd container ratio is 7 : 3. All the three mixtures are mixed in a big container. The ratio of spirit and water in the resultant mixture is ?

Solution(By Examveda Team)

In 2 litres of first container,
Spirit = $$2 \times \frac{4}{5} = \frac{8}{5}$$
water = $$2 \times \frac{1}{5} = \frac{2}{5}$$

In 3 litres of first container,
Spirit =$$3 \times \frac{11}{15} = \frac{11}{5}$$
water = $$3 \times \frac{4}{15} = \frac{4}{5}$$

In 4 litres of first container,
Spirit =$$4 \times \frac{7}{10} = \frac{14}{5}$$
water = $$4 \times \frac{3}{10} = \frac{6}{5}$$

∴ Required ratio
$$ = \left( {\frac{8}{5} + \frac{{11}}{5} + \frac{{14}}{5}} \right) : \left( {\frac{2}{5} + \frac{4}{5} + \frac{6}{5}} \right) $$
$$ = \frac{{33}}{5} : \frac{{12}}{5} $$
= 33 : 12
= 11 : 4