Vessels A and B contain mixtures of milk and water. The ratios of milk and water in A and B are 4 : 5 and 3 : 1, respectively. In what ratio should the contents of A and B be drawn and mixed, to obtain a mixture having milk and water in the ratio 3 : 2?

The ratio of milk and water in A is 4:5, and in B is 3:1

Let us assume that in A, the volume of milk and water is 4x and 5x (total volume is 9x).

For B, the volume can be assumed as 3y and y (total volume is 4y).

After mixing A and B, we get the ratio of milk and water as 3:2

This means, $$\frac{\ (4x+3y)\ }{(5x+y)}$$ = $$\ \frac{\ 3}{2}$$

From the above equation, we get$$\ \frac{\ x}{y}$$as $$\ \frac{\ 3}{7}$$

Hence, the volume of A becomes 27, and that of B becomes 28. 

This makes the ratio of A and B as $$\ \frac{\ 27}{28}$$.