Question

The average age of a group of six children is 15 years. From the group, two children, whose ages were 3 years more and 5 years more than the average age, left. 4 new children, whose average age is 4 years more than the given average age, join the group. Find the new average age.
(a) 15 years
(b) 16 years
(c) 17 years
(d) 18 years
(e) 12 years

Answer 1

I have given the answer below.

And that's 16 years

Answer 2

Solution:

Total Students in the group = 6

Average age = 15 years

Sum of ages of all the students
$15 = \frac{sum \: of \: ages}{total \: numbers} \\ \\ sum \: of \: ages \: = 15 \times \: 6 \\ \\ = 90 \: years$
Now two students left the group= 6-2= 4

Age of first Student => 15+3 = 18 years
Age of second Student => 15+5= 20 years

Now sum of ages of 14 students =90-20-18

=52years

After joining 4 new students ,total students in the group = 4+4=8

each student age is 15+4 = 19 years

Sum of ages of all the students

$52 + 19 \times 4 \\ \\ = 128$

So,new average age
$= \frac{128}{8} \\ \\ = 16$

New Average age is 16 years.

Thus option B is correct.

Hope it helps you.