You have one ₹ 1 coin in your piggy bank. Your father decides to give you daily as many ₹1 coins as you have in the piggy bank. That is, on day one he gives you one ₹1 coin, on day two he gives you two ₹1 coins,on day three he gives you four ₹1 coin, and so on. If your piggy bank becomes full in sixteen days, in how many days would it be 1/8th full..?

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Answers

2014-11-21T18:43:17+05:30

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     1/8 = (1/2)^3   =>  3 days before it becomes full, the piggy bank contains 1/8th of full amount.

==========================  explanation

Number of coins in the bank, after adding coins given by father: 

     day 0 : 1    day1: 2          day2:  4      day3:  8        day 4:  16

Number of coins in the piggy bank after father gives the coins on day n is = 2^n
 
        2^16 =  bank is full
        2^15  =  piggy bank is 1/2 full
        2^14  =  it is 1/4 full
        2^13  =   it is 1/8 full.



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