Group a consists of x students and their total age is 221 and their average age is an integer. when group a is merged with group b with twice the number of students (the number of students between 30 and 40) average age of b is reduced by 1.what is the original average age of b?

16 years

Step-by-step explanation:

Given,

Number of students in group A = X,

Sum of their ages = 221,

So, the average age of students in group A =

According to the question,

∴ X must be a factor of 221,

∵ 221 = 13 × 17,

Now, If X = 13,

Then the number of students in group B = 26 ( NOT POSSIBLE )

If X = 17,

Then the number of students in group B = 34

Which is between 30 and 40,

Now, Let S be the sum of ages of students in group B,

So, the average age in group B =

Again according to the question,

Therefore, the average age of B = = 16 years.

hope this !