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The average age of 24 students is 15.5 years. The age of the teacher is 24 years more than the average age of all the students and teacher. What is the age (in years) of the teacher?
Average = $$\frac{\text{sum of the all terms}}{\text{number of terms}}$$
Total age of 24 students = 24 $$\times 15.5 $$= 372
let the age of teacher be x years.
Average age of all students and teacher = $$\frac{372 + x}{25}$$
According to question,
x = 24 + $$\frac{372 + x}{25}$$
x = $$\frac{600 + 372 + x}{25}$$
x = 972/24 = 405
Therefore age of the teacher is 40.5 years.
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