In three vessels each of 50 litres capacity, mixture of milk and water is filled. The ratio's of milk and water are 1 : 2, 3 : 1 and 3 : 2 in the three respective vessels. If all the three vessels are emptied into a single vessel. find the proportion of milk and water in the mixture?

In the 1st vessel, milk = $$\frac{1}{3}\times\ 50=\frac{50}{3}L$$
In the 2nd vessel, milk = $$\frac{3}{4}\times\ 50=\frac{75}{2}L\ $$
In the 3rd vessel, milk = $$\frac{3}{5}\times\ 50=30L\ $$.
Total milk in the mixture = $$\frac{50}{3}+\frac{75}{2}+30\ =\frac{100+225+180}{6}=\frac{505}{6}L\ $$.
Water = Total - milk = $$150-\frac{505}{6}=\frac{395}{6}\ L$$.
Ratio of milk and water = $$\frac{505}{6}:\frac{395}{6}=101:79$$.