Question

# 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?

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.

In the question, it is given that:
Amount of money that Ajay put on first day = Re.1
And it is given in the question that everyday he doubles the money that he puts in the envelope. So, to calculate the amount of money that he puts on the next day we just multiply the previous day amount by 2.
So, the amount of money that he puts each of days is given as follow:
Amount of money that he puts on the first day $= {\text{Re}}{\text{.1}}$.
${\text{Amount of money that he puts on second day = 2}} \times {\text{amount of money that he puts on first day}} \\ {\text{ = 2}} \times 1{\text{Rupee = Rs}}{\text{.2}} \\ {\text{Amount of money that he puts on third day = 2}} \times {\text{amount of money that he puts on second day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.2 = Rs}}{\text{.4}} \\ {\text{Amount of money that he puts on fourth day = 2}} \times {\text{amount of money that he puts on third day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.4 = Rs}}{\text{.8}} \\ {\text{Amount of money that he puts on fifth day = 2}} \times {\text{amount of money that he puts on fourth day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.8 = Rs}}{\text{.16}} \\ {\text{Amount of money that he puts on sixth day = 2}} \times {\text{amount of money that he puts on fifth day}} \\ {\text{ = 2}} \times {\text{Rs16 = Rs}}{\text{.32}} \\ {\text{Amount of money that he puts on seventh day = 2}} \times {\text{amount of money that he puts on sixth day}} \\ {\text{ = 2}} \times {\text{Rs}}{\text{.32 = Rs}}{\text{.64}} \\ {\text{Amount of money that he puts on eighth day = 2}} \times {\text{amount of money that he puts on seventh day}} \\ {\text{ = 2}} \times {\text{Rs64 = Rs}}{\text{.128}} \\$
So, total money that he collected till 8th day = sum of money collected on each day
= Re.1+Rs.2+Rs.4+Rs.8+Rs.16+Rs.32+Rs.64+Rs.128
= Rs.255.
Note:
In this type of question, the usual method is to calculate the amount for each day by doubling the amount of previous day and then add the amount of each day to get the final answer. But we can also ask this type of question using geometric progression. In this question, it is given that money doubles everyday. So, the common ratio(r)=2 and first term is given 1 and number of terms(n)=8. So, the money collected after 8th day is given by:
${\text{Sum of money = }}\dfrac{{a({r^n} - 1)}}{{r - 1}} = \dfrac{{1({2^8} - 1)}}{{2 - 1}} = {\text{Rs}}.255$