Question : Directions: The average age of 19 boys in a class is 21 years. If the teacher's age is included, the average increases to 22 years. What is the teacher's age?
Option 1: 39 years
Option 2: 41 years
Option 3: 40 years
Option 4: 44 years
Correct Answer: 41 years
Solution :
Given:
The average age of 19 boys in a class is 21 years.
Average⇒(Sum of ages of 19 boys) ÷ 19 = 21
So, the sum of the ages of 19 boys = 19 × 21 = 399
The average age of 19 boys and the teacher is 22 years.
Average (including teacher's age)⇒(Sum of ages of 19 boys + Age of the teacher) ÷ 20 = 22
⇒(Sum of ages of 19 boys + Age of the teacher) = 22 × 20 = 440
Substitute the sum of the ages of 19 boys by 399 (calculated above)
⇒399 + (Age of the teacher) = 22 × 20 = 440
⇒Age of the teacher = 440 – 399 = 41 years
So, the age of the teacher is 41 years. Hence, the second option is correct.
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