In a class,the average age of 41 students is 13.5 years.If the age of the teacher is added to the total ages of the students,then the average age increases by 6 months. Find the age of the class teacher. Options=
(1)43 years 6months. (2)34 years 6 months. (3)35 years 6 months (4) 36 years 6 months.
Answers
The age of the class teacher is option (2): 34 years 6 months.
Step-by-step explanation:
Required formula:
- Average = [Sum of observation] / [No. of observation]
No. of students = 41
The average age of 41 students = 13.5 years
∴ The total ages of 41 students = 13.5 * 41 = 553.5 years
Let the age of the teacher be denoted as “x” years.
According to the question, we can write the eq. as,
[553.5 + x] / 42 = 13.5 + (6/12)
⇒ [553.5 + x] / 42 = 13.5 + ½
⇒ [553.5 + x] / 42 = 14
⇒ 553.5 + x = 42 * 14
⇒ 553.5 + x = 588
⇒ x = 588 - 553.5
⇒ x = 34.5
⇒ x = 34 years 6 months ← the age of the class teacher
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