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?

Question

anonymous · Answer

$$221=13\times 17$$ so there are either 13 students and the average age is 17 or there are 17 students and the average is 13. but since group B has twice the number and it is bigger than 30 we know group A has 17 students and average age is 13

anonymous · Answer

therefore group B has 34 students, total number of students is 51 put total age in group B as x, then the equation to solve is 
$$\frac{221+x}{51}=\frac{x}{34}-1$$

anonymous · Answer

get x = 544 and so average os 
$$\frac{544}{34}=16$$