Question : The average age of 24 students is 15.5 years. The teacher's age is 24 years more than the average age of all the students and teachers. What is the age (in years) of the teacher?
Option 1: 40
Option 2: 41.4
Option 3: 42
Option 4: 40.5
Correct Answer: 40.5
Solution :
Let the age of a teacher be $x$.
average of 24 students = 15.5 years
According to the question
$\frac{15.5 × 24 + x}{25}$ = $x - 24$
⇒ 15.5 × 24 × $x$ = 25$x$ – 24 × 25
⇒ 25$x$ – $x$ = 24 × 25 + 15.5 × 24
⇒ 24 $x$ = 24(25 + 15.5)
⇒ $x$ = 40.5
Hence, the correct answer is 40.5.
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