Question

average age of a group of 50 students was increased by 6 months when group of 10 students was replaced by a group of 10 new students whose average age was 15 years find the average age of new group girls​

Answer 1

Answer:

The average of new group of girls is 151

Step-by-step explanation:

Given as :

The average age of old 50 students = A years

i.e $x_1+x_2+x_3+...........+x_50$ = 50 A

Average age of a group of 50 students was increased by 6 months when group of 10 students was replaced by a group of 10 new students

So, The average of 50 new students

$\dfrac{z_1+z_2+.....+z_50}{50}$ =  (A + $\dfrac{1}{2}$ ) years

i.e $\dfrac{z_1+z_2+z_3+......z_40}{50}$ + 3 = A + $\dfrac{1}{2}$

Or, $\dfrac{z_1+z_2+z_3+......z_40}{50}$ = A - $\dfrac{5}{2}$

i.e $z_1+z_2+.......+z_40$ = 50 ( A - $\dfrac{5}{2}$ )

And The average of 10 new students

$\dfrac{y_1+y_2+y3+.........+y_10}{10}$ = 15

So, The average of new group

150 - (A - $\dfrac{5}{2}$ ) + 150 = A + $\dfrac{1}{2}$

i.e 150 - A + $\dfrac{5}{2}$ + 150 = A + $\dfrac{1}{2}$

Or, 300 + $\dfrac{5}{2}$ - $\dfrac{1}{2}$ = 2 A

Or, 300 + $\dfrac{4}{2}$ = 2 A

Or, 300 + 2 = 2 A

i.e 2 A = 302

∴ A = $\dfrac{302}{2}$

Or A = 151

Hence, The average of new group of girls is 151 Answer