Question

The average weight of the students of a class is $60kg$. If eight new students of average weight $64kg$ join the class, the average weight of the entire class becomes $62kg$. How many students were there in the class initially?

• A. $8$
• B. $12$
• C. $16$
• D. $24$

Answer 1

The correct option is A $8$

Average weight of $x$ students in the class $=60$
$=>\frac{\text{Sum of weights of}x\text{students}}{x}=60$
$=>$ Sum of weights of $x$ students $=60x$
Also given, Average weight of $8$ students $=64$
$=>\frac{\text{Sum of weights of}8\text{students}}{8}=64$
$=>$ Sum of weights of $8$ students $=512$
Now, total weight of the $(x+8)$ students in the class $=60x+512$
Given, average of the final entire class $=62$ kg
$=>\frac{60x+512}{x+8}=62$
$=>60x+512=62x+496$
$=>2x=16$
$=>x=8$
So, there were $8$ students in the class originally.