Mixture and alligation

Question

Two vessels a and b contains milk and water respectively the volume of milk in a and the volume of water in b are in the ratio 4:5. Now x litres of milk from A is poured into b and then y litres of the solution from b is poured into a. If as a result the concentration of milk in a and that of water in b both dropped from 100% to 66 2/3% find x:y

Answer 1

volumes of milk in a and water in b are in a ratio of 4:5

x liters of a are poured into b

then y liters of b are poured into a

resulting percentages of milk and water dropped from 100% to 66 2/3%, A now 2/3 milk, B 2/3 water

what is ratio of x/y??

say there was 120 L milk in A, and 180 L water in B

(120-x+y)/120 = 2/3

360 -3x+3y = 240

120-x+y = 80

y-x = 40

let x= 40, y = 80

A goes from 120 to 80 L milk

B goes from 180 to 260 mixture of 80/260 milk 4/13th milk 9/13ths water= about 69% water

then A goes to 80L milk to 160L mixture of 80L milk +(4/13)(80) = 80('17)/13

A's mixture is 80(17)/13(160 = 17/26 milk = about 66% milk

ratio of x/y = 40/80 = 1/2

B