A man sells apples. First he gives half of the total apples what he has and a half apple. Then he gives half of the remaining and a half apple. He gives it in the same manner. After 7 times all are over. How many apples did he initially have.

• Ans. 127
  
  let the no. of apples intially he had = x
  At first time, he is left with = x/2 - 1/2 = (x-1)/2 no. of apples
  At second time, he is left with = (x-1)/4 - 1/2 = (x-3)/4 no. of apples
  At third time, he is left with = (x-3)/8 - 1/2 = (x-7)/8 no. of apples
  At fourth time, he is left with = (x-7)/16 - 1/2 = (x-15)/16 no. of apples
  At fifth time, he is left with = (x-15)/32 - 1/2 = (x-31)/32 no. of apples
  At sixth time, he is left with = (x-31)/64 - 1/2 = (x-63)/64 no. of apples
  At seventh and last time, he is left with = (x-63)/128 - 1/2 = (x-127)/128 no. of apples
  and this is equals to zero bcoz the process ends now
  (x-127)/128 = 0
  x-127 = 0
  x = 127
• 12 years agoHelpfull: Yes(44) No(0)
• Try to get the formaula by iterative method.
  However in these cases the answer will be 2^n -1.
  so,here the answer will be 2^7 - 1= 127.
• 12 years agoHelpfull: Yes(35) No(5)
• 127
  127 will be ans
• 9 years agoHelpfull: Yes(2) No(3)
• come from the bck as 1,2,4,8,16,32,64 the total is 127
• 9 years agoHelpfull: Yes(1) No(4)