Shortcut Trick
Number of Boys = 39 − 26 = 13. Ratio of Girls : Boys = 26 : 13 = 2 : 1.
Deviation of Girls average (42) from Class average (48) = −6.
Total deviation for 2 units of girls = 2 × (−6) = −12.
To balance, deviation for 1 unit of boys must be +12.
Average weight of boys = 48 + 12 = 60 kg.
∴ The correct answer is 60 kg.
Alternate Method
Given: Total students = 39, Girls = 26, Avg weight of girls = 42 kg, Avg weight of class = 48 kg.
Formula: Total Weight = Average × Number of students
⇒ Number of Boys = 39 − 26 = 13
⇒ Total weight of the class = 39 × 48 = 1872 kg
⇒ Total weight of girls = 26 × 42 = 1092 kg
⇒ Total weight of boys = 1872 − 1092 = 780 kg
⇒ Average weight of boys = 780 ÷ 13
⇒ Average weight of boys = 60 kg
∴ The correct answer is 60 kg.
Additional Information
Weighted Average Formula
The combined average of two groups is given by Aavg = (n1w1 + n2w2) ÷ (n1 + n2), where n is the count and w is the weight.
Deviation Method
The sum of deviations of all observations from the mean is always zero. This helps in finding missing values quickly without large multiplications.
Rule of Alligation
(Quantity of Cheaper) ÷ (Quantity of Dearer) = (Rate of Dearer − Mean Rate) ÷ (Mean Rate − Rate of Cheaper).