The average of a certain set of 'b' numbers is 'a', and the average of a ce1tain set of 'a' numbers is 'b'. What is the average of all the numbers taken together?

2ab ÷ (a + b)

Average of set of b numbers = a

Average of set of a numbers = b

Average = Total sum of values ÷ Number of values

Sum of set of b numbers = Average × Total values

Sum of set of b numbers = a × b = ab

Sum of set of a numbers = b × a = ba

Total Sum of all numbers = ab + ba = 2ab

Total values = a + b

Average of all numbers = 2ab ÷ (a + b)