Puzzle 123 - Leaky container

An explorer Dr. Franz was trekking across a desert in search of a secret treasure. But the water container in his jeep was leaky. 

In the first hour, the container lost half of the water plus one litre. In the second hour it again lost half of the remaining water plus one litre. In the third and fourth hour same thing repeated. But by the end of fourth hour, the container was empty.

How much water did the container originally hold?

 

Answer = 30 liters

 

Let us say there was x liters of water to start with. 

First hour he lost x/2 liters +1 

First hour remaining water was x - (x/2+1) = x/2 - 1

 

Second hour he lost (x/2-1)/2  + 1 = x/4 -1/2+1 = x/4 +1/2

Second hour remaining water was x/2 -1 - (x/4 +1/2) = x/4 - 3/2

 

Third hour he lost( x/4 - 3/2 )/2 +1 = x/8 +1/4

Third hour, the remaining water was x/4 - 3/2 - x/8-1/4 = x/8 - 7/4

 

Fourth hour he lost (x/8 - 7/4)/2 +1 = x/16- 7/8 + 1 = x/16 + 1/8

Fourth hour, the remaining water is x/8-7/4 - x/16- 1/8 = x/16 - 15/8

This is 0

=> x/16-15/8 = 0

=> x/16 = 15/8

=> x = 15/8 * 16 = 30 liters

The original question appeared in the book "Brain teasers" by Ian Livingstone and Jamie Thomson