The average age of a nursery class is 3 years. After half semester, 10 new students with an average age 2.5 years are included in the same nursery class due to which average of the class becomes 17/6 years. Find the number of students initially in the class.?

Question

The average age of a nursery class is 3 years. After half semester, 10 new students with an average age 2.5 years are included in the same nursery class due to which average of the class becomes 17/6 years. Find the number of students initially in the class.?

10
5
7
12
20

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 5 : 20

Average = (sum of elements)/(number of elements)

Let the number of students initially in the nursery class be N.

Given,

The average age of a nursery class is 3 years -

The total sum of ages of all students in the nursery class

= 3N

Given,

10 new students with an average age 2.5 years are included in the same nursery class

Total sum of ages of 10 new students = 10 × 2.5 = 25 years

The total sum of ages of all students including new students

= 3N + 25

The average age of a class with new students = 17/6

⇒ 17/6 = (3N + 25/(N + 10)

⇒ 17(N + 10) = 6(3N + 25)

⇒ 17N + 170 = 18N + 150

⇒ N = 20

∴ Number of students initially in the nursery class is 20

There will be no change in the average 3 years after half semester there is no special condition provided for it. So the average will be 3 before 10 new students join the class.