Average

1.     The average age of a group of people is increased by 10 when a person aged 19 years is replaced by a new person aged 59 years. How many people are there in the group?

Answer:

Let the number of people in the group be = n

Let the total age of the people be = S

So, average age = S/n = K, say

Also, (S – 19 + 59)/n = K + 10

Or, S/n + 40/n = K + 10

Or, K + 40/n = K + 10

Or, 40/n = 10

Or, n = 40/10 = 4