The capacities of three containers X, Y and Z are 1, 2 and 4 litres respectively. Initially X is empty, while Y
and Z are full of water and milk respectively. X is filled from Y. Y is replenished from Z and X is emptied
ito Z. If this process is repeated once more, then what will be the ratio of milk in Y to water in Z?
Answers
Given : The capacities of three containers X. Y and Z are 1, 2 and 4 litres respectively. Initially X is empty, while Y and Z are full of water and milk respectively. X is filled from Y, Y is replenished from Z and X is emptied
into Z. this process is repeated once more
To Find :what will be the ratio of milk in Y to water in Z
Solution:
X(1) Y(2) Z(4)
M=0 W= 0 M=0 W = 2 M = 4 W = 0
X is filled from Y M=0 W= 1 M=0 W = 1 M = 4 W = 0
Y is filled from Z M=0 W= 1 M= 1 W = 1 M = 3 W = 0
X is emptied in Z M=0 W= 0 M= 1 W = 1 M = 3 W = 1
Milk and water in Y are in 1:1 ratio hence 1 litre will have 0.5 Water & 0.5 milk
X is filled from Y M=0.5 W= 0.5 M=0.5 W = 0.5 M = 3 W = 1
Milk and water in Z are in 3:1 ratio hence 1 litre will have 0.25 Water & 0.75 milk
Y is filled from Z M=0.5 W= 0.5 M=1.25 W = 0.75 M = 2.25 W = 0.75
X is emptied in Z M=0 W= 0 M=1.25 W = 0.75 M = 2.75 W = 1.25
Milk in Y = 1.25
Water in Z = 1.25
1.25 : 1.25 = 1 : 1
ratio of milk in Y to water in Z = 1 : 1
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