Question

The average (arithmetic mean) of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. What is the number that was removed

Answer 1

let one number = x

sum of 6 numbers = average × 20 = 120

if x is removed ,  

sum of remaining 5 numbers = 120 - x

average of 5 numbers = (120 -x)/5

given that new average = 15

⇒ (120 - x )/5 = 15

⇒ 120 - x = 75

⇒ x = 120 -75 = 45

45 is the number that is removed