Shortcut Trick Total reduction in the sum of weights of 43 students = 43 × 0.5 = 21.5 kg. This reduction occurs because the new student weight is added to the total. New Average = Weight of joining student + Reduction in total weight of original students New Average = 49 + 21.5 = 70.5 kg. ∴ The correct answer is 70.5 kg. Alternate Method Given: Initial students = 43, Weight of new student = 49 kg, Average reduction = 0.5 kg. Let the new average weight of the class be 'x' kg. ⇒ Total number of students after joining = 43 + 1 = 44 ⇒ Old average weight = (x + 0.5) kg ⇒ Total weight of 44 students = 44 × x ⇒ Total weight of 43 students = 43 × (x + 0.5) According to the question: ⇒ Total weight of 44 students = (Total weight of 43 students) + (Weight of new student) ⇒ 44x = 43(x + 0.5) + 49 ⇒ 44x = 43x + 21.5 + 49 ⇒ 44x − 43x = 70.5 ⇒ x = 70.5 kg ∴ The correct answer is 70.5 kg. Related Concepts: Average Basic Formula Average = Total Sum of Observations ÷ Number of Observations. Inclusion of a New Member If a new member joins and average decreases by 'd', then New Average = New Member Weight + (Old Number × d). Weighted Average When two groups are combined, Combined Average = (n_(1)x_(1) + n_(2)x_(2)) ÷ (n_(1) + n_(2)).