The average weight of a certain number of students in a class is 68.5 kg. If 4 new students having weights 72.2 kg, 70.8 kg, 70.3 kg and 66.7 kg join the class, then the average weight of all the students increases by 300 g. The number of students in the class, initially, is:

As per the question,

The average weight of the students=68.5Kg

Let total number of students in the class =n and weight of the students $$=w_n$$

So, average weight of n students $$\dfrac{w_n}{n}=68.5$$

As per the condition given in the question, $$\dfrac{w_n+72.2+70.8+70.3+66.7}{n+4}=68.5+0.3$$

$$\Rightarrow 68.5n+72.2+70.8+70.3+66.7=68.8\times (n+4)$$

$$\Rightarrow 68.5n+280=68.8n+275.2$$

$$\Rightarrow 68.8n-68.5n=280-275.2$$

$$\Rightarrow 0.3n=4.8$$

Hence the required number of students $$n=16$$