In a class with a certain number of students, if one student weighing 30 kg is added, then the average weight of the class increases by 1 kg. If one more student weighing 30 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 27.
Let the number of students in the class be n and the average weight of n students be x.
Total weight = Average weight × Number of students
Total weight = nx
According to the given question,
nx + 30 = (n + 1)(x + 1)
⇒ nx + 30 = nx + n + x + 1
⇒ n + x = 29 ....(i)
Also, nx + 30 + 30 = (n + 2)(x + 1.5)
⇒ nx + 60 = nx + 1.5n + 2x + 3
⇒ 1.5n + 2x = 57 ...(ii)
Multiplying equation (i) by 1.5 and subtracting equation (i) from equation (ii),
⇒ 2x - 1.5x = 57 - 43.5
⇒ 0.5x = 13.5
⇒ x = 27