Question

Saurabh has reunited with his friends. His friend asked him "Please tell me how many children you have." Saurabh replied: "I have three of them." The Friend: "What are the ages of your children?". He answers: "The product of the ages is equal to 72." The Friend replies: "This is not enough information dear!". "Sorry that I was a little bit unclear, but the sum of the ages is equal to your daughter’s age," says Saurabh. The friend: "This still isn't enough information!". Saurabh replies: "My oldest child loves chocolate." The friend: "Thanks for your cooperation, I now know the ages." What is the age of the youngest child of Saurabh

Answer 1

Given : Saurabh has reunited with his friends.

His friend asked him "Please tell me how many children you have." Saurabh replied: "I have three of them."

The Friend: "What are the ages of your children?".

He answers: "The product of the ages is equal to 72."

The Friend replies: "This is not enough information dear!".

"Sorry that I was a little bit unclear, but the sum of the ages is equal to your daughter’s age," says Saurabh.

The friend: "This still isn't enough information!".

Saurabh replies: "My oldest child loves chocolate."

The friend: "Thanks for your cooperation,

I now know the ages."

To Find  : What is the age of the youngest child of Saurabh

Solution:

Product of ages = 72

( 1 , 1 , 72) , ( 1 , 2 , 36) , ( 1 , 3 , 24) , ( 1, 4 , 18) , ( 1, 6 , 12) , ( 1 , 8 , 9)

( 2, 2 , 18) , ( 2, 3 , 12) , ( 2 , 4 , 9) , ( 2 , 6 , 6)

(3 , 3 , 8 ) , ( 3 , 4 , 6)  

Sum of Each case  

( 1 , 1 , 72) ,    = 74

( 1 , 2 , 36) ,  = 39

( 1 , 3 , 24) , = 28

( 1, 4 , 18) ,  = 23

( 1, 6 , 12) , = 19

( 1 , 8 , 9)  = 18

( 2, 2 , 18) , = 22

( 2, 3 , 12) ,   = 17

( 2 , 4 , 9) ,  = 15

( 2 , 6 , 6)  = 14

 (3 , 3 , 8 ) ,  = 14

( 3 , 4 , 6)   = 13

sum of the ages is equal to   daughter’s age

Hence sum must be 14   as he still do not know age and only sum 14 comes 2 times , all other sums are unique

2  , 6 ,  6

3 , 3 ,  8  

are the options

Saurabh replies: "My oldest child loves chocolate.

He did not say oldest children   as case of 2  , 6 ,  6

Hence 3 , 3 ,  8   is the only remaining option.

Age of his children are 3 , 3 & 8  Years

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