The proportion of milk and water in $3$ samples is $2:1,\,3:2$ and $5:3$. A mixture comprising of equal quantities of all $3$ samples is made. The proportion of milk and water in the mixture is

To maintain equal quantities while combining the three samples, find the least common multiple of the total parts in each ratio, which is 24 for the sums 3, 5, and 8. The first sample has 16 parts milk and 8 parts water, the second has 14.4 parts milk and 9.6 parts water, and the third has 15 parts milk and 9 parts water. Adding these together gives 45.4 parts milk and 26.6 parts water. Multiplying both quantities by 5 to clear the decimals results in a final ratio of 227 to 133 for milk to water.

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