Question

The average age of 10 student and their teacher is 20 years. If the teacher's age is excluded , their average are reduces by 2 years. What is the teacher's age ?

Answer 1

average age of 10 students and teacher =20

sum of ages of 11 people = 20×11 =220

average age of 10 students = 20-2 =18

sum of ages of 10 students = 18×10=180

ageof teacher = 220-180 =40 years

Answer 2

The teacher's age is 40 years.

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Let's understand a few concepts:

To calculate the teacher's age we will use the basic formula of an average i.e.,:

$\boxed{\bold{Average = \frac{Sum\:of\:all\:terms}{Total\:no.\: of \:terms} }}$

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Let's solve the given problem:

Let,

"x" years be the teacher's age.

"S₁" years be the sum of the ages of 10 students.

Including the teacher's age:

The no. of terms = No. of students + 1 teacher = 10 + 1 = 11

The average age of 10 students and a teacher = 20 years

The sum of ages of 10 students and a teacher = (S₁ + x) years

Therefore, we can form the equation as,

$\frac{S_1 \:+\:x}{11} = 20$

$\implies S_1 \:+\:x = 20\times 11$

$\implies S_1 \:+\:x = 220$ . . . (1)

Excluding the teacher's age:

The no. of students = 10

If the teacher's age is excluded, the average age of the teacher and 10 students is reduced by 2 years.

So, the average age of 10 students = 20 - 2 = 18 years

Therefore, we can form the equation as,

$\frac{S_1 }{10} = 18$

$\implies S_1= 18\times 10$

$\implies S_1= 180$ . . . (2)

On substituting equation (2) in equation (1), we get

$180\:+\:x = 220$

$\implies x = 220 - 180$

$\implies \bold{x = 40}$

Thus, the teacher's age is 40 years.

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