A Man would like to take a new health insurance.An officer taking care of these matters says to the man: "Please tell me how many children you have". The Man answers : "I have three of them ." The officer :"What are the ages of the children?" The Man answers :"The product of the ages is equal to 36." The officer replies:"This is not enough information Sir!!" ; The Man replied"Sorry that I was a little bit unclear, but the sum of the ages is equal to the number of shops in front of your office." The officer:"This still is not enough information Sir!"; The man replies :"My oldest child loves chocoalate." The officer:"Thanks for your cooperation, I now know the ages".
Are you a smart officer? Then what are the ages of the children.
A. 1, 4, 9
B. 2, 2, 9
C. 1, 3, 12
D. 2, 3, 6

• The product of the ages is 36. So, following combination of ages are possible:
  
  1, 1, 36 | sum = 38
  1, 2, 18 | sum = 22
  1, 3, 12 | sum = 16
  1, 4, 9 | sum = 14
  1, 6, 6 | sum = 13
  2, 2, 9 | sum = 13
  2, 3, 6 | sum = 11
  3, 3, 4 | sum = 10
  
  When man had said that the product of the ages is equal to 36, the officer didn't have enough information. When the man said that the sum of their ages equals to number of shops in front of the office the officer could not again still understand because there must be more than one such combination possible. In fact from the above, we can see it can only be 13. So the sum of the ages should be 13, because otherwise he would have known the ages immediately. The last statement is that that the oldest child loves chocolate. So there is an oldest child. Hence the officer concludes that the ages of the children are 2, 2 and 9 years.
• 9 years agoHelpfull: Yes(20) No(2)
• Among 6 possibilties for 36 only 1×6×6 and 2×9×2 gives equal sum of their individuals i.e 13 thats y officer get confused among these two ... bt after knwing tht ther is oldest one , it was easy for him to guess 2 2 9 ANS.
• 9 years agoHelpfull: Yes(8) No(0)
• answer is 1,4,9
  
  the product is equal to 36 which is satisfied by every option
  
  the sum of the ages is equal to the shops infront of the office
  
  the sum of different options are 14,13,16,11
  
  person can become confuse between 13 n 14 but not between 11 n 14 or 16 n 11
  
  so the last two options are ruled out
  
  as the man says my oldest duaghter the option 2 is also ruled out because if it 2,2,9 then he only have to say my older daughter so the answer is 1,4,9
• 9 years agoHelpfull: Yes(4) No(10)
• @avantika ....See Officer Knows already that How many Shops Infront Of His Office, and That Man Gives Clue That Sum of ages is equal to shop infront of ur office.....So officer knew that age sum is 13 But officer have again Confusion Because, In Possiblities 1,6,6 and 2,2,9 Sum Is 13. so agian asked to man an man replied that my oldest child love chocolates so officer understand it...1,6,6 two big number (he said oldest means only 1 children who having highest age) here two highest number, wheres 2,2,9 having one highest number means oldest child age. So, Ans is 2,2,9. Got It ?
• 9 years agoHelpfull: Yes(3) No(2)
• but how do we know that der are 13 shops?
• 9 years agoHelpfull: Yes(3) No(0)
• @subham how sum of the ages is 13?
• 9 years agoHelpfull: Yes(2) No(0)
• @awantika.. there are two possibilities 1,6,6 or 2,2,9
  among these for first case ie. 1,6,6, two elder daughters have same ages... but in second case ie 2,2,9 there is only one elder daughter ... 9
• 9 years agoHelpfull: Yes(1) No(1)
• @prateek -> oldest means older among all...
• 9 years agoHelpfull: Yes(0) No(1)
• how does 1 know abt oldest?@Priyank
• 9 years agoHelpfull: Yes(0) No(1)
• The product of the ages is 36. So, following combination of ages are possible:
  
  1, 1, 36 | sum = 38
  1, 2, 18 | sum = 22
  1, 3, 12 | sum = 16
  1, 4, 9 | sum = 14
  1, 6, 6 | sum = 13
  2, 2, 9 | sum = 13
  2, 3, 6 | sum = 11
  3, 3, 4 | sum = 10
  
  When man had said that the product of the ages is equal to 36, the officer didn't have enough information. When the man said that the sum of their ages equals to number of shops in front of the office the officer could not again still understand because there must be more than one such combination possible. In fact from the above, we can see it can only be 13. So the sum of the ages should be 13, because otherwise he would have known the ages immediately. The last statement is that that the oldest child loves chocolate. So there is an oldest child. Hence the officer concludes that the ages of the children are 2, 2 and 9 years.
• 5 years agoHelpfull: Yes(0) No(0)