Question

The average age of a class of 39 students is 15 years .if the age of the teacher be included, then the average increases by 3 months .find the age of the teacher. (arithmetic aptitude)


a. 25 years b. 27 years c. 35 years d. 28 years

Answer 1

25 years.I hope you got it.

Answer 2

Answer:

25 years.

Step-by-step explanation:

The average age of a class of 39 students is 15 years

$Average = \frac{\text{Sum of ages of 39 students}}{\text{No. of students}}$

$15 = \frac{\text{Sum of ages of 39 students}}{39}$

$15 \times 39 =\text{Sum of ages of 39 students}$

$585=\text{Sum of ages of 39 students}$

If the age of the teacher be included, then the average increases by 3 months

12 months = 1 year

1 month = $\frac{1}{12} years$

3 months = $\frac{1}{12} \times 3 years$

3 months = $\frac{1}{4} years$

Average becomes :  $15+\frac{1}{4} years$

                                   $15.25 years$

Let the age of teacher be x

Total no. of students + one teacher = 39+1 = 40

Sum of ages of 39 students + age of teacher = 585+x

So, $15.25 = \frac{585+x}{40}$

$15.25 \times 40 =585+x$

$610 =585+x$

$610-585=x$

$25=x$

So, option A is true.

Hence  the age of the teacher is 25 years.