Question

The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. If the initial average is 14 years, find the age of the class teacher

Answer 1

$24 \: years \: is \: the \: age \: of \: the \: teacher$

For Solution,
Please refer the above photograph for the used process!



KEY POINTS TO REMEMBER :-


☸️ Average is the sum of observations divided by number of observations.
So,

$average = \frac{sum \: of \: data}{number \: of \: data}$



☸️ To derive the sum of observations from the number of observations and Average, we need to multiply the two.

Thus,
$sum \: of \: data = average \times frequency$



☸️ In the above question, we have two cases.
One with teacher and another without teacher.
So,. We can obtain the teacher's age by subtracting the sum of ages of the two cases.

So,

Refer to the above photograph for the used process of solving the problem...


Thanks!

Answer 2

Answer:

shortcut:

The teacher after fulfilling the average of 14 (for the group to which he belonged) is also able to give 0.5 years to the age of each of the 30 students. Hence, he has 30x 0.5 = 15 years to give over and above maintaining his own average age of 14 years.

Age of teacher = 14 + 30 x 0.5 = 29 years.

(Note: This problem should be viewed as change of average from 13.5 to 14 when teacher is included.)

for shortcut method (IMAGE)click the drive link.(due to image uploading restrictions on brainly) . screenshot the link and copy the link using GOOGLE LENS.

https://drive.google.com/file/d/1_pevuF6e07WMI-mO4ktHmekV-8q2-iHY/view?usp=drivesdk