Average

The average age of a group of 10 students is 24.
∴ the sum of the ages of all 10 of them = 10 × 24 = 240
When two students joins the group, the average increase by 1. New Average = 25
Now there are 11 students ∴ sum of all the ages of 12 students = 12×25 = 300
∴ the sum of the ages of two students who joined = 300 - 240 = 60
And the average age of these two students = 30

By question, we should calculate from C's age

C = 5 years 2 months
From the age of C, the age of B can be written as
B = (5 + 3) years (2 + 4) months
= 8 years 6 months
From the age of B, the age of A can be written as
A = (8 + 4) years (6 + 7) months
= 12 years 13 months
(12 months become 1 year)
A = 13 years 1 month
Average = (A + B + C)/3
= (8 + 5 + 13) years (6 + 2 + 1) months/3
= (26 years 9 months)/3
(balance 2 years become 24 months
So, 24 + 9 = 33)
= 8 years 11 months
∴ average = 8 years 11 months

The average age of a group of 10 students is 18.
∴ the sum of the ages of all 10 of them = 10 × 18 = 180
When two students joins the group, the average increase by 1. New Average = 19
Now there are 12 students ∴ sum of all the ages of 12 students = (12 X 19 ) =228
∴ the sum of the ages of two students who joined = 228 - 180 = 48
And the average age of these two students = 24

Let number of non-teaching staff be x.
Average salary of all staff = ₹ 10,000
Average salary of 20 teaching staff = ₹ 12,000
Average salary of non-teaching staff = ₹5000
Since, Average salary of teaching staff + Average salary of no-teaching staff = Average salary of all staff
(20×12000) + (x×5000) = (x + 20)×10000
240000 + 5000x = (x + 20)×10000
Divide the equation 1000,
240 + 5x = (x + 20)×10
240 + 5x = 10x + 200
10x - 5x = 240 - 200
5x = 40
x = 8

The average age of a group of 10 students is 22.
∴ the sum of the ages of all 10 of them = 10 × 22 = 220
When two students joins the group, the average increase by 1. New Average = 23
Now there are 12 students
∴ sum of all the ages of 12 students = 12 X 23 = 276
∴ the sum of the ages of two students who joined = 276 - 220 = 56
And the average age of these two students = 28

The average age of a group of 10 students is 20.
∴ the sum of the ages of all 10 of them = 10 × 20 = 200 When two students joins the group, the average increase by 2. New Average = 22
Now there are 12 students ∴ sum of all the ages of 12 students = (12 X 22) = 264
∴ the sum of the ages of two students who joined = 264 - 200 = 64
And the average age of these two students = 32

The average age of a group of 10 students is 10.
∴ the sum of the ages of all 10 of them = 10 × 10 = 100
When two students joins the group, the average increase by 1.
New Average = 11
Now there are 12 students
∴ sum of all the ages of 12 students = 132
∴ the sum of the ages of two students who joined = 132 - 100 = 32
And the average age of these two students = 16

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