A container contains 64 litres of milk. From this container 16 litres of milk was taken out and replaced by water. This process was repeated overall three times. How much milk is now contained by the container?

Question: A container contains 64 litres of milk. From this container 16 litres of milk was taken out and replaced by water. This process was repeated overall three times. How much milk is now contained by the container?

Solution:
After first replacement the ratio of milk and water is 48 : 16 = 3 : 1

After second replacement,
remaining milk = 48 - (3/4 of 16) = 48 - 12 = 36
water = 16 +12= 16 + 12 = 28
∴ ratio = 36 : 28 = 9 : 7

After third replacement,
remaining milk = 36 - (9/16 of 16) = 36 - 9 = 27
water = 28 + 9 = 37
∴ ratio = 27 : 37

shortcut,
after three replacement the reamining milk will be = 64 × (3/4)³
= 64 × 27/64
= 27