Five men checked into a hotel with a bag of peanuts and a monkey. They planned on dividing the peanuts evenly the following morning. However, during the night, one of the men got up, divided the peanuts into five equal parts, took his fifth and had one leftover peanut which he gave to the monkey. He put the other shares of peanuts back into the bag and returned to bed. A little later, a second man (who did not know that the first man had been up) divided the peanuts five ways and took his fifth. He also had one peanut left over, which he gave to the monkey and he returned the rest of the peanuts to the bag.
Likewise, during the night the third, fourth and fifth men got up and divided the peanuts, and each had one left over for the monkey. The next morning they divided the remaining peanuts equally five ways. How many peanuts were originally in the bag?
(a) 1641 (b) 1742 (c) 2351 (d) 3121

• ans is 3121
  bcz: by option verification take 3121 peanuts.
  1st person= 3121/5=(624+1)(here 1 is remainder) in this 1 part is taken and remaining 1 is given to monkey so remaining 4 parts =624*4=2496. are replaced in bag
  2nd person.....................
  again 2496/5= (499+1)( here 1 is remainder). again 1 part is taken and remaining 1 is given to monkey.
  remaining 4 parts = 499*4=1996. replaced in bag
  3rd person..........................again 5 parts
  1996/5=(399+1)(here 1 is remainder). given to monkey
  remaing 4 parts= 399*4=1596 remaining replaced in bag
  4th person
  1596/5=(319+1)(1 is remainder given to monkey)
  remaing 4 parts= 319*4=1376 replaced in bag
  5th person
  1376/5=(275+1) 1 is given to monkey
  remaining 4 parts= 275*4=1100
  next morning they equally divided the remaining peanuts 1100/5=220
  so answer is 3121
• 9 years agoHelpfull: Yes(6) No(0)
• can any one explain it clearly pls
  
• 10 years agoHelpfull: Yes(3) No(2)
• option verification is better option
  ans:3121
  
• 11 years agoHelpfull: Yes(2) No(3)
• hey can ny one tell the short cut to this pblm...
• 11 years agoHelpfull: Yes(2) No(3)
• Ans:3121. Take every answer and check according to the question. (By looking in to the ans you can eliminate option (b) because ans should be an odd number)
• 11 years agoHelpfull: Yes(1) No(3)
• According to question peanuts will at the end 30 times because each person is dividing peanut 5 eual parts and this happen 6 times so - 5*6 =30 times.
  now according to question divide given option by 30 what you will get that 1641/30 = 54.7
  so,
  OPTION:- A .1641 must be ans.
• 9 years agoHelpfull: Yes(0) No(3)
• The easiest way to do this is using options
  
  The final answer should be of the form 5k+1 because he has one leftover peanut after making five equal parts
  
  so the only options which remain are 856 and 3121
  
  856-1 =855
  so each equal part 171
  after first man has taken his part
  we have 684 peanuts remaining... which is not of the form 5k+1
  
  hence the only valid option is 3121 which can be checked to be true....
• 9 years agoHelpfull: Yes(0) No(0)
• If n is supposed to be unknown,and Y is total sum and X is last share Then original equation will be:
  
  Y = nX.(n/n-1)^n +((n/n-1)^(n-1)) +((n/n-1)^(n-2)) +----------- +((n/n-1)^2 )+(n/n-1) +1
  
  if n=5, and let Y and X is unknown
  then
  Y=5X.(5/5-1)^5 +((5/5-1)^5-1) +((5/5-1)^5-2) +((5/5-1)^5-3) +((5/5-1)^5-4)+((5/5-1)^5-5).
  resolving the equation
  Y=15.25878906X+8.20703125
  
  if it is simplifyed -- withot decimals /divisions
  the equation becomes
  15625X + 1024Y = 8404
  
  in both the equation if we put X=204
  then Y=3121.
• 9 years agoHelpfull: Yes(0) No(2)