The ratio of water and alcohol in two different containers is 2:3 and 4:5. In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7:5?

Given:

• Container A: Water : Alcohol = 2 : 3 ⇒ Alcohol fraction = 3 / (2+3) = 3/5 = 0.6
• Container B: Water : Alcohol = 4 : 5 ⇒ Alcohol fraction = 5 / (4+5) = 5/9 ≈ 0.555
• Required ratio (Alcohol : Water) = 7 : 5 ⇒ Alcohol fraction = 7 / (7+5) = 7/12 ≈ 0.583

Apply the alligation rule:

Alcohol in A      = 0.6  
Alcohol in B      = 0.555  
Desired alcohol   = 0.583

Alligation method:

           A         B
         0.6       0.555
           \       /
            \     /
           0.583
            /     \
           /       \
      0.583 - 0.555 = 0.028
      0.6   - 0.583 = 0.017

Required ratio = 0.028 : 0.017 = 28 : 17

Simplify to lowest whole-number match with options:

28 : 17 ≈ 5 : 3

Answer: 5 : 3

So, the mixtures must be combined in the ratio 5:3 (Container A : Container B).