Correct Answer - Option 1 : 55 kg
Given:
There are total 15 students in a class.
An old student of weight 25 kg was replaced by the new student.
New average weight is more than the old average weight by 2 kg.
Concepts used:
Average weight = (Total weight of all students)/(Number of students)
Calculation:
Let the original average weight of students be x kg.
So, Total weight of all students = 15x
According to the question
New average weight = x + 2 kg
Let the weight of the new student be y kg.
New total weight of 15 students = Original total weight of all students + Weight of new student - weight of old student
⇒ (15x + y – 25) kg
Average weight = Total weight of all students/Number of students
⇒ x + 2 = (15x + y – 25)/15
⇒ 15 × (x + 2) = 15x + y – 25
⇒ 15x + 30 = 15x + y – 25
⇒ y = 30 + 25 = 55 kg
∴ The weight of new student is 55 kg.
