A container originally contains 10 litres of pure spirit. From this container, 1 litre of spirit is replaced with 1 litr...

Question

A container originally contains 10 litres of pure spirit. From this container, 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

A. 7.29 litres   B. 7.00 litres   C. 7.31 litres   D. 7.29 litres

Accepted Answer

D. 7.29 litres of spirit remain after three replacements. Each time we remove 1 litre of mixture from a 10-litre container, we remove the current fraction of spirit in the mixture, then replace that volume with water. This is the classic dilution formula: after each step the spirit is multiplied by (9/10). After three steps we apply (9/10)^3.