Question

Consider a class of 23 students. The average age of a student in the class is 12 years. If the age of the teacher is also included, then the average age of the class is increased by 7 months.
What is the age of the teacher ?
(a) 24 years
(b) 26 years
(c) 23 years
(d) None of the above​

Answer 1

Answer:

26 : Answer

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Good question

Answer 2

Answer :

option (b) 26 years

Step-by-step explanation :

$\underline{\underline{\bf Mean:}}$

⇒ It is the average of the numbers.

⇒ Add up all the terms and divide the number of terms in the data set.

⇒ The mean of x₁, x₂, x₃ ,..., xₙ

$\bf Mean=\frac{x_1+x_2+x_3+...+x_n}{n}$

⇒ Mean = sum of observations/number of observations

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we know,

$\bf Average=\frac{\textbf{Sum of observations}}{\textbf{Number of observations}}$

Given,

The average age of a student in a class of 23 students is 12 years.

• Average age of student = 12 years = 12 × 12 months = 144 months
• Total number of students = 23

here,

$\bf Average \ age \ of \ a \ student=\frac{Sum \ of \ 23 \ students' \ age}{total \ no.of \ students}$substituting the values, $\bf 144 \ months =\frac{\textbf{Sum of 23 students' age}}{23} \\\\ Sum \ of \ 23 \ students' \ age=(144 \times 23) \ months \\\\ Sum \ of \ 23 \ students' \ age=3312 \ months$

∴ Sum of 23 students' age = 3312 months (i.e., 276 years)

Also given,

If the age of the teacher is also included, then the average age of the class is increased by 7 months.

Now,

Average age of the class = (144 + 7) months = 151 months

Total number of members in the class

= 23 + 1

= 24

So,

$\bf Average \ age \ of \ the \ class=\frac{Sum \ of \ 23 \ students' \ age+age \ of \ the \ teacher}{total \ no.of \ members \ in \ the \ class}\\ \\ Substituting \: the \: values, \\ \\ \bf 151 \ months=\frac{3312 \ months +age \ of \ the \ teacher}{24} \\\\ 3312 \ months +age \ of \ a \ teacher=151 \times 24 \ months \\\\ 3312 \ months +age \ of \ a \ teacher=3624 \ months \\\\ age \ of \ the \ teacher=(3624-3312) \ months \\\\ age \ of \ the \ teacher=312 \ months \\\\ age \ of \ the \ teacher=(312/12) \ years \\\\ age \ of \ the \ teacher=26 \ years$

Therefore, age of the teacher = 26 years