The average age of the class of 30 student increases by one year when

1.	The average age of the class of 30 student increases by one year when 15 new students join. What is the difference in the average age of the new students to the new average of the class?1. 32. 23. 44. 5
Answer» Correct Answer - Option 2 : 2 Given: The average age of the class of 30 students increases by one year when 15 new students join. Formula: Average of n numbers a1, a2, ..., an = (a1 + a2 + ... + an)/n Calculation: Let the average age of the class be x. Total age of 30 students = 30x New average age of the class after joining 15 students = x + 1 Total age of 45 students = 45 × (x + 1) Let the average age of 15 new students be y. Total age of 15 students = 15y According to question 45(x + 1) = 30x + 15y ⇒ 45x + 45 = 30x + 15y ⇒ 15x + 45 = 15y ⇒ y – x = 3 The difference in the average age of the new students and the new average of the whole class = y – (x + 1) = (x + 3) – (x + 1) = 2 The difference in the average age of the new students and the new average of the class is 2 years.

The average age of the class of 30 student increases by one year when 15 new students join. What is the difference in the average age of the new students to the new average of the class?1. 32. 23. 44. 5

Answer» Correct Answer - Option 2 : 2

Given: The average age of the class of 30 students increases by one year when 15 new students join.

Formula: Average of n numbers a1, a2, ..., an = (a1 + a2 + ... + an)/n

Calculation:

Let the average age of the class be x.

Total age of 30 students = 30x

New average age of the class after joining 15 students = x + 1

Total age of 45 students = 45 × (x + 1)

Let the average age of 15 new students be y.

Total age of 15 students = 15y

According to question

45(x + 1) = 30x + 15y

⇒ 45x + 45 = 30x + 15y

⇒ 15x + 45 = 15y

⇒ y – x = 3

The difference in the average age of the new students and the new average of the whole class =

y – (x + 1) = (x + 3) – (x + 1) = 2

The difference in the average age of the new students and the new average of the class is 2 years.