Question

If you had the choice of a salary of Rs. 1000 a day for a month of 31 days(choice 1) or Rs.1 for the first day's work, Rs. 2 for the second, Rs. 4 for the third and each day thereafter for the rest of the month, your salary would be doubled(choice 2),

which choice would you make ?

Answer 1

In choice 1, the total salary for the month will be Rs. $31000$
For choice 2, salary will be $1+2+....+2^{30}$ which is equal to $2^{31}-1$
Now, we know that $2^9$ is $512$ and so, $2^{18}$ will be ${512}^2$, which will be greater than $250000$
Hence, the number $2^{31}-1$ will obviously be greater than $31000.$
Hence, we will prefer choice 2.