Two vessels, A and B contain 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 liters of milk from A is poured into B and the y liter 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.
Answers
Given : volume of milk in A and the volume of water in B are in the ratio 4:5. Now, x liters of milk from A is poured into B and the y liter 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%
To find : x:y.
Solution:
Volume of milk = 4P
Volume of Water = 5P
x litre of milk poured into B
Concentration water reduced to 66 2/3 % = 200/3 % = 2/3
Hence 5P/(5P + x) = 2/3
=> 15P = 10P + 2x
=> 2x = 5P
=> x = 5P/2
Now in B - Milk = 5P/2 & water = 5P & total 15P/2
y litre is added from B to A
Milk = Y(5P/2)/(15P/2) = y/3
Water = 2y/3
And already milk in A = 4P - 5P/2 = 3P/2
Now milk = 3P/2 + y/3
total = 3P/2 + y
Concentration milk reduced to 66 2/3 % = 200/3 % = 2/3
=> ( 3P/2 + y/3)/(3P/2 + y) = 2/3
=> 9P/2 + y = 3P + 2y
=> 3P/2 = y
x = 5P/2 & y = 3P/2
x : y = 5 : 3
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