Saturday 10 January 2015

A Thirst Problem



             Rajiv and Sanjiv went camping .they took their own water in big plastic bottle.
             Rajiv got thirsty and drank half the water in his bottle. A little later on he drank 1/3 of what was left. Some time afterwards he drank ¼ of what remained and so on.

          Sanjiv also had a bottle of the same size. He drank half the bottle at the first instance, half of what remained when he drank next and so on.

           After each took ten drinks the water Rajiv had left was how many times greater than the water Sanjiv had left?
Answer:  1024 / 11 times.
                                                                               R has left                                  s has left

                      End of one drink                                        ½                                             ½ 

1/11     1/2¹⁰  End of two drinks                                     1/3                                          (1/2)²

                            End of three drinks                             ¼                                             (1/2)³ 

                           End of four drinks                              1/5                                             (1/2)⁴

                           End of five drinks                               1/6                                         (1/2)⁵        
    
                           End of six drinks                                1/7                                           (1/2)⁶

2¹⁰ / 11   = 1024 / 11           end of seven drinks           1/8                                            (1/2)⁷

                                      End of eight drinks                1/9                                             (1/2)⁸

                                     End of nine drinks                   1/10                                           (1/2)⁹

                                     End of ten drinks                     1/11                                        (1/2)¹⁰

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