Question

The average age of 10 students and their teachers is 20 years.If the teacher's age is excluded , their average age reduces by 2 years.what is the teacher's age ?​

Answer 1

Answer:

The teacher is 40 years old.

Step-by-step explanation:

Average of 10 students and teacher = 20

Average of 10 students = 18

Total age of the 10 students = 180 (18 x 10)

Total age of the students and teacher = 220 (20 x 11)

220 - 180 = 40

Hence, the teacher's age is 40.

Answer 2

Therefore the teacher’s age is 40 years.

The average age of 10 students and their teacher is 20 years. If the teacher’s age is excluded, their average age reduces by 2 years.

We have to do the teacher’s age.

Let the teacher’s age is x.

we know,

“average is the ratio of sum of observations to the number of observations.”

∴ average age of 10 students and a teacher = 20

⇒(sum of students’ age + age of teacher)/(10 + 1) = 20

⇒sum of students’ age + x = 11 × 20

⇒sum of students’ age + x = 220 ...(1)

now teacher’s age is excluded, their average age is reduced by 2.

∴ new average age = initial average age - 2

⇒ sum of students’ age/10 = 20 - 2

⇒ sum of students’ age/10 = 20 - 2

⇒ sum of students’ age = 18 × 10

⇒sum of students’ age = 180 ...(2)

putting equation (2) in equation (1) we get,

⇒ 180 + x = 220

⇒x = 220 - 180 = 40

Therefore the teacher’s age is 40 years.