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In a school, the average age of 39 students of class 10th students is 16 years. If we include the age of the class teacher, then the average increases by 3 months. The age of the class teacher is
In a school, the average age of 39 students of class 10th students is 16 years. If we include the age of the class teacher, then the average increases by 3 months. The age of the class teacher is
1). 30 years
2). 26 years
3). 35 years
4). 25 years
1 answers
2 vote
Average age of 40 persons including teacher = 16 years 3 months
$(\Rightarrow 16 + \frac{3}{{12}} = 16 + \frac{1}{4} = \frac{{65}}{4}{\rm{\;years}})$
We know,
$(Average = \frac{{Sum\;of\;all\;observations}}{{Number\;of\;observations}})$
⇒ Sum of all observations = Average × Number of observations
Total age of 39 students = 39 × 16 = 624 years
Also,
Total age of 40 persons = (65/4) × 40 = 650 years
∴ Age of the teacher = 650 years – 624 years = 26 years