Puzzle 77 | The better choice

Many students applied for a technical job for a month(April) but only two among them successfully completed the technical rounds. It was time for the final Interview. The interviewer asked both the students whether they would like to have 10 crores rupees for the month or, Re. 1 on day 1, Rs. 2 on day 2, Rs. 4 on day 3 , doubling up everyday till the last day of the month.
Student 1 chose 10 crore rupees. Student 2 chose the other option.
Which student made a better choice and how much was the profit?

Solution: Student 2 made a better choice.

Explanation: Student 1 chose 10 crore rupees. Congratulations to that student! It is a lot of money but about 97.4 crore rupees lesser than what student 2 had opted for.
Student 2 will get Re. 1 on day 1, Rs. 2 on day 2, Rs. 4 on day 3 ….The amount sequence is a geometric progression – 1,2,4,8,16,…..and so on.
Total no. of terms = 30 (April has 30 days)

G.P. summation formula for n terms having first term a and common ratio r : a( (r^n) -1 ) / (r-1)

Here a= 1 , r=2, n=30
Sum = (2^30 -1)/(2-1) = 1073741823

Profit = 1073741823 – 10,00,00,000 = 97,37,41,823

This puzzle is contributed by Feroz Baig. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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