abhasjha wrote:Group A consist of x students and their total age is 221 and their average is a integer.when group A is merged with group B with twice the number of students (number of students between 30 and 40 ) average age of B is reduced by 1. What is the original average of B ?
(a) 14
(b) 15
(c) 16
(d) none of these
Total of the ages in Group A = (number of students)I(average age per student) = 221.
Since 221 = 13*17, the number of students in Group A must be 1, 13, or 17.
Since Group B has twice the number of students, and the number of students in Group B must be between 30 and 40, only one case is possible:
Number of students in Group A = 17.
Number of students in Group B = 2*17 = 34.
Since there are 17 students in Group A, and the sum of their ages = 221, the average age of the students in Group A = 13.
We can plug in the answers for the average age of the students in Group B.
When the groups are combined, there will be twice as many students from B as from A.
Thus, of every 3 students, 2 students will be from Group B, while 1 student will be Group A.
Implication:
To determine the average age when the groups are combined, we need only compute the average age when 2 students from B are combined with 1 student from A.
Answer choice D: 16
Here, the 2 students from Group B will have an average age of 16, while the 1 student from Group A will be 13 years old.
Average age for the 3 students = sum/number = [(2*16) + 13]/3 = 15.
(average age for Group B) - (average for the groups combined) = 16-15 = 1.
Success!
The correct answer is
C.
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