JAMB Mathematics 2020 Paper

Concept:The mean changes because the teacher’s age is added to the total age and the number of people increases by one.Explanation:Let $N$ be the number of students.The total age of the students is $15N$.When the $45$-year-old teacher is added, the new total age is $15N + 45$.The new number of people is $N + 1$.The new mean age is $18$, so:$$\frac{15N + 45}{N + 1} = 18$$Multiply both sides by $N + 1$:$$15N + 45 = 18(N + 1)$$$$15N + 45 = 18N + 18$$Collect like terms:$$18N - 15N = 45 - 18$$$$3N = 27$$$$N = \frac{27}{3} = 9$$Answer:There are $\boxed{9}$ students in the group, so the correct option is B.