Mixtures Alligation

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

  1. 27 : 14
  2. 27 : 13
  3. 27 : 16
  4. 27 : 18

Answer

Concentration of milk in the first bottle is 7/9 and that in the second bottle is 9/13. They need to be mixed in a certain ratio to get a solution which has 3/4 milk. 

Applying alligation,

(Liquid taken from bottle 1) / (Liquid taken from bottle 2)

= (9/13 - 3/4) / (3/4 - 7/9)

= 27/13

The correct option is B.