Shortcut Trick
Weight of new person = Weight of replaced person + Total increase in weight
Total increase in weight = Increase in average × Total persons
Total increase in weight = 1.2 × 15 = 18 kg
Weight of new person = 51 + 18 = 69 kg
∴ The correct answer is 69 kg.
Alternate Method
Given:
Number of persons = 15
Increase in average weight = 1.2 kg
Weight of the replaced man = 51 kg
Formula Used:
New member value = Replaced member value + (Increase in average × Total members)
Replaced Man (51 kg)
Total Increase
15 × 1.2 = 18 kg
New Man = 51 + 18 = 69 kg
Average Replacement Concept
Calculations:
⇒ Let the initial average weight of 15 persons be A.
⇒ Total initial weight = 15 × A
⇒ When a 51 kg man is replaced by a new man of weight W, the new average becomes (A + 1.2).
⇒ New total weight = 15 × (A + 1.2)
⇒ New total weight = 15A + 18
⇒ Also, New total weight = Total initial weight − 51 + W
⇒ 15A + 18 = 15A − 51 + W
⇒ 18 = W − 51
⇒ W = 51 + 18
⇒ W = 69 kg
∴ The correct answer is 69 kg.
Additional Information
Replacement in Averages
If a new value replaces an old value and the average increases: New Value = Old Value + (Increase × n).
Addition in Averages
If a new member joins and the average increases: New Member Value = Old Average + (Increase × New n).
Removal in Averages
If a member leaves and the average decreases: Leaving Member Value = Old Average + (Decrease × New n).