In a class of a certain number of students, if a student weighing 30 kg joins, the average weight increases by 1 kg. If another student weighing 30 kg joins, the average increases by 1.5 kg over the original average. What was the original average weight of the class?
Show answer & explanation
Correct answer: B
Explanation
Given:
Weight of each new student = 30 kg
Increase in average when 1 student joins = 1 kg
Increase in average when 2 students join = 1.5 kg
Formula:
Average = (Total Weight) / (Number of Students)
Assuming the original number of students = n
Original Average = A
Total Weight = nA
If 1 student joins
(nA + 30) / (n + 1) = A + 1
nA + 30 = (n + 1)(A + 1)
30 = n + A + 1
A = 29 − n
If 2 students join
(nA + 60) / (n + 2) = A + 1.5
nA + 60 = (n + 2)(A + 1.5)
60 = 1.5n + 2A + 3
57 = 1.5n + 2A
Substituting A = 29 − n
57 = 1.5n + 2(29 − n)
57 = 1.5n + 58 − 2n
57 = 58 − 0.5n
0.5n = 1
n = 2
A = 29 − 2 = 27 kg