The average weight of 10 students is increased by half a kg when one of the students weighing 51 kg is replaced by a new student. Find the weight of the new student.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 56 kg.
Let the initial average weight of the 10 students be 'x' kg.
Let the weight of the new student be 'y' kg.
Calculate the initial total weight:
⇒ Initial total weight = 10 × x = 10x kg
Calculate the new total weight:
⇒ New total weight = Initial total weight - Weight of replaced student + Weight of new student
⇒ New total weight = 10x - 51 + y kg
Calculate the new average weight:
⇒ New average weight = Initial average weight + 0.5 kg
⇒ New average weight = x + 0.5 kg
Set up the equation:
⇒ New total weight / Number of students = New average weight
⇒ (10x - 51 + y) / 10 = x + 0.5
Solve the equation:
⇒ 10x - 51 + y = 10x + 5
⇒ y = 5 + 51
⇒ y = 56 kg
Therefore, the weight of the new student is 56 kg.