Question

The average age of 25 students and the principal is 16
years. When the principal's age is excluded, the average
age decreases by 2 year. What is the age of the
principal?​

Answer 1

Answer:

Age of principal is 66 years

Step-by-step explanation:

[ Refer to the attachment ]

Answer 2

Answer:

Age of principal is 66 years.

Given Data:  

Average age of 25 students and the principal is 16 years.  

To Find:

To calculate the age of principal:

Explanation:

Step 1:

Let the ages of 25 students be $x_{1}, x_{2}, \ldots \ldots x_{25}$ and the principal’s be y.  

Step 2:

Given $\frac{\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\cdots \ldots \ldots+\mathrm{x}_{25}+\mathrm{y}}{26}=16$

$x_{1}+x_{2}+x_{3}+\cdots \ldots \ldots+x_{25}+y=416 \quad \ldots \ldots(i)$

Step 3:

When principal’s age is excluded  

$\frac{\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\cdots \ldots \ldots+\mathrm{x}_{25}}{25}=14$

$x_{1}+x_{2}+x_{3}+\cdots \ldots \ldots \ldots+x_{25}=350 \quad \ldots \ldots(i i)$

Step 4:

Substitute the equation of (ii) in (i)

350 + y = 416

Y = 416 - 350

Y = 66

Step 5:

Age of principal is 66 years.