A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process ofpouring out two-thirds the content and replacing with water is repeated three more times, then the finalratio of milk to water in the glass, is

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Question :

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of
pouring out two-thirds the content and replacing with water is repeated three more times, then the final
ratio of milk to water in the glass, is

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0 10

A.
1 : 27
B.
1 : 80
C.
1 : 81
D.
1 : 26

Option B is the correct answer.

Explanatory Answer

Final concentration of milk $=$ Initial concentration * $(1 - (x / v))^{n}$
$x =$ volume replaced
$v =$ total volume
$n =$ number of iterations
Let initial quantity of milk $= y$ litres
Final concentration $= y (1 - 2 / 3)^{4} = y (1 / 3)^{4} = 1 / 81 y$
Volume of milk $= 1 / 81 y$
Volume of water $= y - (1 / 81 y) = 80 / 81 y$
Final ratio of milk to water in the glass $= 1 : 80$