Question : In a class of 60 students, there are 35 boys. The average weight of boys is 42 kg and the average weight of the full class is 46.5 kg. Find the average weight of girls in the class.
Option 1: 48.7 kg
Option 2: 49.7 kg
Option 3: 52.8 kg
Option 4: 56.7 kg
Correct Answer: 52.8 kg
Solution :
Let the average weight of girls in the class be $x$
Given the average weight of boys = 42 kg
Number of boys = 35
The average weight of the class = 46.5 kg
Total number of students = 60
So, the number of Girls = 60 – 35 = 25
The sum of weight of boys = Average weight of boys × Number of boys
The sum of weight of girls = Average weight of girls × Number of girls
The average weight of class = $\frac{\text{Sum of the weight of boys and girls}}{\text{Total number of students}}$
$\therefore$ $46.5=\frac{35\times 42 + x\times 25}{60}$
⇒ $2790=1470+25x$
⇒ $x=\frac{1320}{25}$
$\therefore x=52.8$
Hence, the correct answer is 52.8 kg.
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