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# To save money for a video game, Ajay puts 1 rupee in an envelope. Each day for a total of 8 days he doubles the number of rupee from the day before. How much will he save on the eighth day?

Last updated date: 15th Mar 2023
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Hint: In the question, it is given that on the first day Ajay puts 1 rupee and for the next coming days he doubles the amount of money everyday. So, start with 1 rupee and then double the amount of money everyday that he puts into the envelope and then add them all for eight days to get money collected on the 8th day.

Amount of money that he puts on the first day $= {\text{Re}}{\text{.1}}$.
${\text{Amount of money that he puts on second day = 2}} \times {\text{amount of money that he puts on first day}} \\ {\text{ = 2}} \times 1{\text{Rupee = Rs}}{\text{.2}} \\ {\text{Amount of money that he puts on third day = 2}} \times {\text{amount of money that he puts on second day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.2 = Rs}}{\text{.4}} \\ {\text{Amount of money that he puts on fourth day = 2}} \times {\text{amount of money that he puts on third day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.4 = Rs}}{\text{.8}} \\ {\text{Amount of money that he puts on fifth day = 2}} \times {\text{amount of money that he puts on fourth day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.8 = Rs}}{\text{.16}} \\ {\text{Amount of money that he puts on sixth day = 2}} \times {\text{amount of money that he puts on fifth day}} \\ {\text{ = 2}} \times {\text{Rs16 = Rs}}{\text{.32}} \\ {\text{Amount of money that he puts on seventh day = 2}} \times {\text{amount of money that he puts on sixth day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.32 = Rs}}{\text{.64}} \\ {\text{Amount of money that he puts on eighth day = 2}} \times {\text{amount of money that he puts on seventh day}} \\ {\text{ = 2}} \times {\text{Rs64 = Rs}}{\text{.128}} \\$
${\text{Sum of money = }}\dfrac{{a({r^n} - 1)}}{{r - 1}} = \dfrac{{1({2^8} - 1)}}{{2 - 1}} = {\text{Rs}}.255$