Answer : Option C

Explanation :

Let the quantity of vessels A and B in the ratio x: y to form a mixture of water and milk in the ratio 4: 5.
Or, Milk: water = 5: 4.
From vessel A, milk: water = 4x/9: 5x/9
From vessel B, milk: water = 5y/6: 1y/6

Now, ATQ quantities of the mixture should be taken from A and B.
Ratio of milk: water = [4x/9 +5y/6]: [5x/9+ 1y/6] = 5/4
Take the LCM of 9 and 6 = 54
Or, [24x + 45y]/54: [30x+9y]/54 = 5/4
Or, [8x + 15 y]: [10x + 3y] = 5/4
Or, [8x + 15y] * 4 = [10x + 3y] * 5
Or, (60-15) y = (50-32) x
Or, 45y = 18x
Or, 5y = 2x
Or, x: y = 5: 2
Hence, the quantity of mixture should be taken from A and B in the ratio 5: 2.