Shortcut Trick Weight of common person (M) = [Sum of individual pairs] − [Total sum] M = 2 × (Avg_(L+M) + Avg_(M+N)) − 3 × (Avg_(L+M+N)) M = 2 × (89 + 96.5) − 3 × 93 M = 2 × 185.5 − 279 = 371 − 279 = 92 kg. ∴ The correct answer is 92 kg. Alternate Method Given: Average weight of (L, M, N) = 93 kg Average weight of (L, M) = 89 kg Average weight of (M, N) = 96.5 kg Formula Used: Total Weight = Average Weight × Number of persons Calculations: ⇒ Total weight of (L + M + N) = 93 × 3 = 279 kg --- (Eq. 1) ⇒ Total weight of (L + M) = 89 × 2 = 178 kg --- (Eq. 2) ⇒ Total weight of (M + N) = 96.5 × 2 = 193 kg --- (Eq. 3) ⇒ Weight of M = (Total weight of L + M) + (Total weight of M + N) − (Total weight of L + M + N) ⇒ Weight of M = 178 + 193 − 279 ⇒ Weight of M = 371 − 279 ⇒ Weight of M = 92 kg ∴ The correct answer is 92 kg. Related Concepts: Average Concept Average = (Sum of all observations) ÷ (Total number of observations). Deviation Method If the average of n terms is A, and one term is part of two overlapping subsets, the term = A + ∑(Deviations). This avoids large multiplications. Weighted Average Combined Average = (n_(1)x_(1) + n_(2)x_(2)) ÷ (n_(1) + n_(2)), where n is the number of items and x is the average of each group.