In set of three numbers, the average of the first two numbers is 7, the average of the last two numbers is 10, and the average of the first and the last numbers is 14. What is the average of the three numbers?

31/3

Let three numbers are :- x , y & z

ATQ,

x + y = 2 × 7 = 14

y + z = 2 × 10 = 20

x + z = 2 × 14 = 28 

On adding all ,

2 ( x + y + z ) =  14 + 20 + 28 = 62

x + y + z = 31

Average of three numbers = \(\frac{31}{3}\)