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A group of three friends, K, L and M, are sitting in a café. 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’, replace ‘K’, then the average age of L, M, N and R becomes 22.5 years. What is the age of K?

A group of three friends, K, L and M, are sitting in a café. 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’, replace ‘K’, then the average age of L, M, N and R becomes 22.5 years. What is the age of K? Correct Answer 24 years

According to the given information,

Average of K, L and M is 24

K + L + M/3 = 24

K + L + M = 72     ...1)

Average of K, L, M and N is 23

K + L + M + N/4 = 23

K + L + M + N = 92     ...2)

Substituting (1) in (2)

72 + N = 92

N = 20

R who is two years older than N replace K

R = 22

Average of R, L, M and N is 22.5

R + L + M + N/4 = 22.5

R + L + M + N = 90

22 + L + M + 20 = 90

L + M = 48

Substituting this in (1)

K + 48 = 72

K = 24

K is 24 years old.

Hence, “24” is the correct answer.

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