# Guess their ages?

**Number Theory**Level 3

A middle-aged couple, Mr and Mrs Tan have four children - Benedict, Bob, Brenda and Brian. Soon after their three sons rode their motorbikes for the first time, Mrs Tan became pregnant with Billy. Then, Mr Tan tried to calculate the average age of everyone in the Tan family and found it to be an integer.

When Billy was just born, Mr Tan did the same again and interestingly ended up with another integer. What is the most likely sum of the ages of everyone in the Tan family?

Assumptions:

No one's birthdays passed between the two times Mr Tan calculated the average age.

The four siblings are listed in order of their birth (i.e. Benedict is the oldest followed by Bob, Brenda and Brian).

When a person is x years and y months old where y is between 0 and 11 inclusive, that person is taken to be x years old even if he/she is due to turn (x+1) years old within the same year.

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