A group of three friends, K, L and M, are sitting in a cafe. Their average age is 24 years. Another friend ‘N’ joins the group and the new average age of the group becomes 23 years. If another friend ‘R’, whose age is 2 years more than that of ‘N’, replaces ‘K’, then the average age of L. M, N and R becomes 22.5 years. What is the age of K?

Average of K, L and M = 24
Sum of the age of K, L and M = 24 $$\times$$ 3 = 72
Average of K, L, M and N = 23
Sum of the age of K, L, M and N = 23 $$\times$$ 4 = 92
Age of N = 92 - 72 = 10
Age of R = 2 + Age of N = 2 +10 = 12
Average age of L, M, N and R = 22.5 years
Sum of age of L, M, N and R = 22.5 $$\times$$ 4 = 90 
Sum of age of L, M and N = 90 - 12 = 78
Age of K = sum of the age of K, L, M and N - sum of age of L, M and N = 92 - 78 = 14