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The average of the ages of 15 students in a class is 19 years. When 5 new students are admitted to the class, the average age of the class becomes 18.5 years. What is the average age of the 5 newly admitted students?
  • a)
    17 years
  • b)
    17.5 years
  • c)
    18 years 
  • d)
    18.5 years
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The average of the ages of 15 students in a class is 19 years. When 5 ...
Let the average age of 5 students be x
Sum of ages of 15 students + Sum ages of 5 students = Sum of ages of 20 students
Sum = Average × Number of observations
15 × 19 + 5 × x = 20 × 18.5
285 + 5x = 370
5x = 85
∴ x = 17 years
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Most Upvoted Answer
The average of the ages of 15 students in a class is 19 years. When 5 ...
Given:
Average age of 15 students = 19 years
New students admitted = 5
New average age of the class = 18.5 years

To find:
Average age of the 5 newly admitted students

Solution:
Let the sum of ages of 15 students be x.
So, the average age of 15 students = x/15 = 19 years
Therefore, the sum of ages of 15 students = 15 × 19 = 285

After the admission of 5 new students, the total number of students becomes 20.
Let the sum of ages of 5 new students be y.
So, the new average age of the class = (x + y)/20 = 18.5 years
Therefore, the sum of ages of 20 students = 20 × 18.5 = 370

Now, we can write an equation:
(x + y) = 370 - - - - - - - - - - - (1)
x/15 = 19
x = 285 - - - - - - - - - - - - (2)

Substituting equation (2) in equation (1), we get:
y = 370 - 285 = 85

Therefore, the average age of the 5 newly admitted students = y/5 = 17 years.

Hence, the correct answer is option (a) 17 years.
Free Test
Community Answer
The average of the ages of 15 students in a class is 19 years. When 5 ...
19-0.5*20/5=17
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The average of the ages of 15 students in a class is 19 years. When 5 new students are admitted to the class, the average age of the class becomes 18.5 years. What is the average age of the 5 newly admitted students?a)17 yearsb)17.5 yearsc)18 yearsd)18.5 yearsCorrect answer is option 'A'. Can you explain this answer?
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