One vessel holds 30 litres of a milk-and-water mixture in the ratio 7 : 3, and another holds 20 litres of a milk-and-water mixture in the ratio 2 : 3. Both vessels are emptied into a drum. In the drum, milk and water are in the ratio:

First vessel: milk $30\times 7/10=21$ L, water 9 L. Second vessel: milk $20\times 2/5=8$ L, water 12 L. The drum holds 29 L of milk and 21 L of water — a ratio of 29 : 21, and 29 + 21 = 50 L as it should be. (Adding the ratio terms straight off as (7 + 2) : $(3+3)=3$ : 2 ignores that the vessels hold different amounts, and 11 : 9 would be right only if equal quantities had been taken from each.)