Shortcut Trick
Assume Total Average = 7200 as the baseline.
Net Deviation for 27 emps = 27 × (4100 − 7200) = 27 × (−3100) = −83700
Net Deviation for 13 emps = 13 × (6100 − 7200) = 13 × (−1100) = −14300
Total deficit to be covered by 2 emps = 83700 + 14300 = 98000
Average salary of 2 emps = 7200 + (98000 ÷ 2) = 7200 + 49000 = 56200
∴ The correct answer is Rs. 56200.
Alternate Method
Given:
Total employees = 42 | Overall Average = Rs. 7200
Group 1 (n1) = 27 employees | Avg1 = Rs. 4100
Group 2 (n2) = 13 employees | Avg2 = Rs. 6100
Remaining Group (n3) = 42 − 27 − 13 = 2 employees
Calculations:
⇒ Total salary of all 42 employees = 42 × 7200 = Rs. 3,02,400
⇒ Salary of 27 employees = 27 × 4100 = Rs. 1,10,700
⇒ Salary of 13 employees = 13 × 6100 = Rs. 79,300
⇒ Salary of remaining 2 employees = 3,02,400 − (1,10,700 + 79,300)
⇒ Salary of remaining 2 employees = 3,02,400 − 1,90,000 = Rs. 1,12,400
⇒ Average salary of remaining 2 employees = 1,12,400 ÷ 2 = Rs. 56,200
∴ The correct answer is Rs. 56200.
Additional Information
Weighted Average Formula
Weighted Average = (n1A1 + n2A2 + ... + nkAk) ÷ (n1 + n2 + ... + nk), where n is the quantity and A is the average.
Net Deviation Principle
In any data set, the sum of deviations of all observations from their arithmetic mean is always zero (Σ(x − x̄) = 0).
Average Change Calculation
If a new person joins and the average increases, the new person's value = Old Average + (Increase × New Total Members).