The average age of 30 students in a class is 14 years. When the teacher's age is included, the average becomes 15 years. What is the teacher's age?

44 yearsCorrect answerYour answer45 yearsCorrect answerYour answer46 yearsCorrect answerYour answer50 yearsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The 30 students together account for $30 \times 14 = 420$ years.
With the teacher there are 31 people averaging 15, so the new total is $31 \times 15 = 465$ years.
The teacher's age is the difference: $465 - 420 = 45$ years.

Worth noting

There is a quicker route. The teacher must supply their own 15 plus one extra year for each of the 30 students whose average rose, giving $15 + 30 = 45$ .

Concept: Effect of one new value on an average
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsChange in average

Practise this chapter →

Ten questions from Averages, at your own pace.

The average age of 30 students in a class is 14 years. When the teacher's age is included, the average becomes 15 years. What is the teacher's age?

Explanation