Question

The average age of a group of students registered to participate in a science forum is 17 years. 10 new students with an average age of 16 years join the forum, due to which the average age of all the students changes to 16.5 years. Find the initial number of students who registered for the forum.
1. 23
2. 30
3. 10
4. 20

Answer 1

Correct Answer - Option 3 : 10

Given:

The average age of the initial number of students = 17 years

When 10 students with an average age of 16 years join, the average becomes 16.5

Formula used:

Average = (Sum of observation)/(Number of observation)

Calculation:

Let the initial number of students be x

Then, according to the formula, we have

Total weight of students = 17x

Now, according to the question, we have

{17x + (10 × 16)}/(x + 10) = 16.5

⇒ 17x + 160 = 16.5x + 165

⇒ 17x - 16.5x = 165 - 160

⇒ 0.5x = 5

⇒ x = 10

∴ Initial number of students was 10.