A bottle containing 10 liters of alcohol one liter of alcohol is removed and replaced with water. After a liter of the mixture was removed and replaced with water, the operation being carried out 7 times in total. Then that amount of alcohol remains in the container.

alcohol removed = 1/10 liter first time

= 1/10 (.9) liter second time
= 1/10 (.9)(.9) third time

....

=1/10 (.9)^6 seventh time
so
amount removed = .1 + .1*.9^1 +....1*.9^6
seven terms
a = .1
sum removed = .1 (1-.9^7)/.1
= .478
so amount remaining = 1-.478 = .522