From a cask of milk containing 64 liters, 8 liters are drawn out, and the cask is filled up with water. If the same process is repeated a second and then a third time, what will be the proportion of milk to water in the remitting mixture?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 343:169.
Amount of milk = Original amount[1 - (Amount replaced by water/Original amount)]n
Where n = number of operations = 3
Milk = 64(1 - 8/64)3 = 64(1 - 1/8)3 = 21952/512 litres
Amount of water = 64 - (21952/512) = 10816/512 litres
Required ratio = (21952/512) : (10816/512) = 343 : 169
Hence, the proportion of milk to water in the remiting mixture is 343 : 169.