puzzle - How much would you have earned?

Friday, December 31, 2010

Question:

If you started a business in which you earned Rs.1 on the first day, Rs.3 on the

second day, Rs.5 on the third day, Rs.7 on the fourth day, & so on.

How much would you have earned with this business after 50 years (assuming

there are exactly 365 days in every year)?

Answer

Rs.333,062,500

To begin with, you want to know the total number of days: 365 x 50 = 18250.

By experimentation, the following formula can be discovered, & used to

determine the amount earned for any particular day: 1 + 2(x-1), with x being the

number of the day. Take half of the 18250 days, & pair them up with the other

half in the following way: day 1 with day 18250, day 2 with day 18249, & so on, &

you will see that if you add these pairs together, they always equal Rs.36500.

Multiply this number by the total number of pairs (9125), & you have the amount

you would have earned in 50 years.

Math gurus may use series formula to solve it.(series: 1,3,5,7,9,11.....upto 18250

terms)