One more Tricky Question

[sridatta]

Once there was a trader in a village who gives money for interest.. Once a young man went to him and asked him money on an agreement.. The agreement is as follows...

Young man will give the merchant 10000 $ / Day for 30 days...
Merchant should give him 1 Cent on 1st day, and double the amount every day.. i.e. 2 cents on 2nd day, 4 cents on 3rd day, 8 cents on 4th day and so on...

The merchant agreed instantly... why ????

[zhinghur]

I think the merchant was fool... He saw (10000 *30)$ but he didnt realise the power of 2.....

It seems to him that , he need to pay just couple of cents doubled per day (2,4,8,16....). But he forgot how much he need to pay at the end of the day ....

At the end of the day he need to pay .......

(2 +2*2 + 2*2*2 + ...........................+ (2*2*2*...upto 30 times))

He will get bankrupt even before, i guess just in 22 days.....


Correct me if i am wrong..........

[zerzis]

Yes ZhinGhur, you are correct.

it's summation of this formula: (2 raise to n) + (2 raise to (n+1)) where n runs from 1 to 30. :)

2 raise to 30 itself is 1073741824 ! :))

[Hurbel2k]

If You were here on this message board without basic mathematic skills I would be very surprised.

[sridatta]

yeah.. ofcourse, its not about solving the problem.. but to learn the fact that.. Business without change in growth will never lead to success..

First curve: Y = 10000 X
Second curve: Y = 2^X

Calculating the growth,
First curve dy/dx = 10000
Second curve dy/dx = (2^x)log 2

similarly, calculating the change in growth
First curve d2y/dx2 = 0

Eventually, the first curve goes to Zero...

Suppose you start a business, and if the profit for every year is the same, then your growth rate is zero.. and you may not succeed as there are other ways where your competetors can take over you.. Initially, 2^x curve will stay below the 10000x line.. But, after sometime, i will overtake the line... hence, if there is good growth rate, it will surely shine some day..

Just assume that you are earning a constant profit and your competetor earns a profit of low amounts, but with a decent growth every year..., ultimately, he will gain more profits after a certain threshold point...

Many business geeks do such calculations to estimate their company growth

Please quote me if i am wrong..

[zerzis]

Sridatta, you have put forward a very important point here. Growth is very important and it doesnt matter what your initial earnings level is. If you are grwoing constantly with the demands of the market then one day you will lead the doamin of your business. This idea has been wel lexplained by the above example, that was very good sridatta, keep it up. :).