Question

The average weight of a class of 20 students is 45 kgs. A new student whose weight is 40 kgs replaces an old student of this class. Hence, the average weight of the whole class decreases by 1 kg. The weight of the replaced student is :

• A. 55 kgs
• B. 50 kgs
• C. 60 kgs
• D. none of these

Answer 1

The correct option is C 60 kgs

Since you know that there are total 20 students and when the average weight decreases by 1, it means on an average 1 kg weight is reduced from each of the students. Thus there is 20 kg weight loss, in total. Again this happens due to the student whose weight is 40 kg replaces an old student. Thus we can say that the weight of the old (or existing) student of the class was 60 kg, which is reduced by a 40 kg student.

Alternatively:
Initially, the total weight = 20 $\times$ 45 = 900
Now, the total weight when a student has been replaced = 20 $\times$ 44 = 880
It means the weight of the new student is 20 kgs less than the replaced student. Hence the weight of the replaced student = 40 + 20 = 60 kgs