The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group. 

A.

7

B.

9

C.

15

D.

42

Correct answer is B

x \(\frac{\sum x}{N}\)

15 = \(\frac{\sum x }{N}\)

\(\sum x\) = 15N........(i)

y = \(\frac{\sum y}{Ny} = \frac{\sum x + 45}{N + 1}\)

\(\frac{18}{1} = \frac{15N + 45}{N + 1}\) 

18(N + 1) = 15N + 45

18N + 18 = 15N + 45

18N - 15N = 45 - 18 

3N = 27 

N = \(\frac{27}{3}\) 

= 9