A container contains 64 litres of pure milk. From this

Solution

Quantity of milk in container after first replacement = 64 - 8 = 56 litres Quantity of water in container after first replacement = 8 litres Ratio of quantity of milk to that of water in the container after first replacement = 56:8 = 7:1 Quantity of milk in 8 litres of mixture taken out in second replacement = (7/8) X 8 = 7 litres So, quantity of milk in the container finally = 56 - 7 = 49 litres Alternate solution If from 'P' litres of pure quantity of liquid 'A', 'q' litres is withdrawn and is replaced by same quantity of another liquid 'B' and the process is repeated 'n' times, then quantity of liquid 'A' left in the mixture can be given by: P X {1 - (q/P)}ⁿ So, required quantity of milk = 64 X (1 – 8/64)² = 64 X (1 - 1/8)² = 64 X {(7 x 7)/(8 x 8)}  = 49 litres