Shortcut Trick
Net deviation from the given average (75 kgs) for the entire group must be exactly zero.
Deviation for the first 10 people = 10 × (70 − 75) = −50 kgs.
Deviation for the next 5 people = 5 × (75 − 75) = 0 kgs.
To balance the total deviation to zero, the remaining 5 people must have a combined deviation of +50 kgs.
Average deviation for these 5 people = +50 ÷ 5 = +10 kgs, making their average weight 75 + 10 = 85 kgs.
∴ The correct answer is 85 kgs.
Alternate Method
Given:
Total number of people = 20
Average weight of 20 people = 75 kgs
Average weight of 10 people = 70 kgs
Average weight of the next 5 people = 75 kgs
Formula Used:
Sum of observations = Average × Number of observations
Total: 20 People | Average: 75 kgs
10 People
Avg: 70 kgs
5 People
Avg: 75 kgs
5 People
Avg: ? kgs
Deviation: 10 × −5 = −50
Dev: 0
Dev: +50
75 + 10 = 85 kgs
Calculations:
⇒ Total weight of all 20 people = 20 × 75 = 1500 kgs
⇒ Total weight of 10 people = 10 × 70 = 700 kgs
⇒ Total weight of the next 5 people = 5 × 75 = 375 kgs
⇒ Weight of remaining 5 people = Total weight − (Weight of 10 people + Weight of next 5 people)
⇒ Weight of remaining 5 people = 1500 − (700 + 375)
⇒ Weight of remaining 5 people = 1500 − 1075 = 425 kgs
⇒ Average weight of remaining 5 people = 425 ÷ 5 = 85 kgs
∴ The correct answer is 85 kgs.
Additional Information
Weighted Average Concept
When separate groups are combined, the overall average is determined using the formula: Combined Average = (n1 × A1 + n2 × A2 + ...) ÷ (n1 + n2 + ...).
Net Deviation Method
The sum of the deviations of all individual elements from their mean value is always perfectly zero. Balancing these deviations serves as a reliable shortcut to finding missing values in a group.