A thief steals half the total no of loaves of bread plus 1/2
loaf from a bakery. A second thief steals half the remaining
no of loaves plus 1/2 loaf and so on. After the 5th thief
has stolen there are no more loaves left in the bakery. What
was the total no of loaves did the bakery have at the beginning

• answer 31
  
  after the 5th = 0
  before 5 th =1
  before 4th =3
  before 3rd =7
  before 2nd =15
  before 1st = 31
• 11 years agoHelpfull: Yes(40) No(31)
• ANS:31
  
  let y be the total number of loaves
  a be the remaining loaves after 1st thief
  b be the remaining loaves after 2nd thief
  e = 0 be the remaining loaves after 5th thief
  a = y - (y/2 + 1/2)
  = y/2 - 1/2
  b = a - (a/2 + 1/2)
  = a/2 - 1/2
  c = b - (b/2 + 1/2)
  = b/2 - 1/2
  d = c - (c/2 + 1/2)
  = c/2 - 1/2
  e = d - (d/2 + 1/2)
  = d/2 - 1/2
  wkt, e = 0,
  thus by subs,
  d = 1
  c = 3
  b = 7
  a = 15
  y = 31
• 10 years agoHelpfull: Yes(32) No(3)
• x=31,they are stealing in amount,(x+1)/2,(x+1)/4,....(x+1)/32,add them and substract it from total x..
  
• 11 years agoHelpfull: Yes(16) No(10)
• answer is 15 as frst theif will tak 1/2t+1/2 second will tak 1/4t+1/4...so on ffth will take 1/32t+1/32...adding and subtracting to t..we get t =15
• 11 years agoHelpfull: Yes(1) No(26)
• plz check yours ans its 31
  
• 8 years agoHelpfull: Yes(1) No(0)
• Let the total no. of loaf be x.
  
  So, the 1st thief stole (x/2 + 1/2) = ( x+1)/2
  The second thief stole ((x+1)/2)/2 + 1/2 = (x+3)/4
  The third thief stole (x+7)/8 and so on.
  
  As there is no bread left after the fifth thief,
  hence, the equation becomes
  
  (x+1)/2 + (x+3)/4 + (x+7)/8 + (x+15)/16 + (x+31)/32 = x
  or, (31x+129)/32 = x
  or, x = 129 (ans)
• 7 years agoHelpfull: Yes(1) No(4)